How Does Drawing Arrays For The Factor Pairs Help You Understand The Turn Around Rule?

How to discover the factors of a number

Leap to

Factors are that divide exactly into a number.
Factors can exist found by listing them out, using or using
A is a ready of two factors. When multiplied together, the pair give a particular . A has one cistron pair consisting of ane factor multiplied by itself.
A number that has more than two factors is a . This can be expressed as a unique . This is useful when finding the (HCF) and (LCM) of big numbers.
To be able to observe factors and write a number as a product of prime factors, having noesis of powers and indices is useful.

Draw different rectangular with the correct amount of squares. Eg, to find the factors of xv, draw arrays with 15 squares
- The beginning rectangle will ever exist ane x the number y'all are finding factors for.
- For the next rectangles, consider whether they tin can have a dimension of two, iii, four etc. Use your understanding of to help.
Each time you describe a rectangle, 2 are establish. These are a
Sometimes one of the rectangles is a square with equal side lengths. This happens when the number is a . The same factor is constitute twice - therefore only one factor is actually found. Eg, 5 × v = 25 and 5 is a factor of 25

Remember: To find all the gene pairs, it is not necessary to draw every rectangle. Eg, a 5 ten two rectangle and a ii x v rectangle are the same rectangle in a different orientation. Just i of these rectangles is needed to become the factor pair of two and five. Either rectangle can be picked.

Fifteen with fifteen blocks below it. — Utilise arrays to find the factors and factor pairs of 15

one of 10

Four diagrams each made-up of fifteen blocks. Two are bars – one is vertical; one is horizontal. Two are grids – one is three by five; one is five by three. — Draw rectangles containing 15 squares. The number of squares forth each side will be a gene of xv

ii of x

The bars are now labelled. The vertical with one at the top and fifteen on the left. The horizontal with fifteen on the top and one of the left. — These rectangles bear witness that 1 x 15 = 15 and fifteen x 1 = 15

3 of x

The grids are now labelled. The vertical grid is labelled with three at the top and five on the left. The horizontal with five on the top and three of the left. — These rectangles prove that 3 x 5 = xv and five ten three = 15

4 of ten

The horizontal bar and grid are faded, while the vertical diagrams stayed the same. — Ii unique rectangles can be fatigued for xv. The i x 15 rectangle is the same as 15 x 1. iii x 5 is the same as 5 x 3

v of ten

The vertical bar and grid. Written to the right. Factors of fifteen. One, three, five, fifteen – all highlighted. Factor pairs of fifteen. One and fifteen – highlighted. Three and five – highlighted. — 15 is a blended number - it has more than ii factors. The factors of 15 are 1, 3, 5 and xv. The factor pairs for 15 are the pairs of dimensions for each rectangle. The factor pairs of 15 are 1 and 15, and 3 and v

six of 10

Example 2: Nine with nine orange blocks below it. — Use arrays to find the factors and gene pairs of 9

vii of ten

Three diagrams each with nine blocks. Two are bars – one is vertical with the top labelled with one and the left labelled with nine; one is horizontal with the top labelled with nine and the left labelled with one. The third is a faded three by three grid. — These rectangles show that 1 x 9 = nine and 9 x 1 = 9. These rectangles give the aforementioned cistron pair, i and 9. Only one of the rectangles is needed - either can be picked.

eight of 10

The vertical bars are faded. The top and left of the three by three grid is now both labelled with three. — This assortment is a square considering the sides are equal in length. The square shows that 3 × 3 = 9. This gives only ane gene, 3

9 of 10

The vertical bar and the grid. Written to the right. Factors of nine. One, three, nine – all highlighted. Factor pairs of nine. One and nine – highlighted. Three and three – highlighted. — The unique arrays are 1 x nine and three 10 3. 9 is a square number and has an odd number of factors - the factors of 9 are 1, 3 and ix. The factor pairs of ix are 1 and ix, 3 and 3

10 of 10

A is fabricated up of that are numbers greater than 1. A number does not produce a gene tree because 1 of its factors is 1 and the other is itself so the number would be repeated – the factor tree would non grow.

Write the number at the superlative of the factor tree.
Draw two branches from the number to separate the number into a pair of factors, greater than 1
Write each gene at the end of each co-operative.
- If a cistron is a prime number, the branch does not extend any further and the gene is circled to evidence this.
- If the cistron is not a prime, it is split into a further pair of factors, greater than 1
This procedure continues until the branches all end in prime number numbers. These are of the number.

Recall : the cistron tree of a number tin expect different, simply the numbers at the end of the branches will be the same .

Thirty with two lines pointing down from it. — Find the prime factors of 30 using a gene tree.

i of 7

The number thirty four times each with two lines pointing down to highlighted numbers. The first points to two and fifteen with a green tick over the thirty. The second points to three and ten with a green tick over the thirty. The third points to five and six with a green tick over the thirty. The last points to one and thirty – all faded – with a red cross of over the top thirty. — Draw two branches from the number xxx to divide it into a pair of factors, greater than 1. The factor pair could be two and 15, 3 and 10 or 5 and 6. The gene pair of ane and 30 is non used because the factor 1 is not greater than 1 and the 30 is repeated.

2 of seven

Thirty with two lines pointing down to five and six – both highlighted. — In this instance the factor pair of v and 6 is used. Write each factor (5 and 6) at the end of each co-operative.

iii of 7

Five is now circled. — 5 is a prime number number so the 5 branch does non extend any further. Circumvolve the five to show this.

4 of vii

Same diagram. Now with two lines pointing down from the 6 to two and three – both highlighted. — half dozen is not a prime number so the gene tree can grow further. half-dozen is divide into a further pair of factors, greater than i. 2 x 3 = 6, and then write the factors 2 and iii at the finish of each branch.

v of 7

Two and three are now circled. — 2 and iii are both prime numbers and so they can be circled. All the branches now cease in prime numbers. The factor tree for 30 is consummate. The prime number factors are 5, 2 and 3

vi of 7

Three diagrams of numbers branching down from thirty. First: Thirty going to two and fifteen. Two is circled. Fifteen going to three and five – both circled. Second diagram: Thirty going to six and 5. Five is circled.. Six going to two and three – both circled. Third diagram: Thirty going to ten and three. Three is circled. Ten going to two and five – both circled. Written below: The prime factors of thirty are two, three and five – all highlighted. — The gene tree for 30 can take different forms, depending on which factors are used at the start. The prime factors are always the same. The prime number factors of 30 are 2, 3 and 5

seven of 7

To write a number equally a , the number is written as the upshot of multiplying its together.

Draw a factor tree.
Write the number equal to the factors multiplied together in numerical order.
When a number occurs more than once, this can as well be written in class (with powers).

Writing a number as a product of its prime factors tin can be helpful when finding the (HCF) and (LCM) of large numbers.

Example 1: A factor tree for 30. This is a diagram of numbers branching from thirty. Thirty going to six and a circled five. Six going to two and three – both circled. — Utilize the gene tree of xxx to write thirty as a product of its prime number factors.

i of 8

Same diagram with the circled numbers five, two and three highlighted. To the right. Thirty equals two multiplied by three multiplied by five. — The prime factors of thirty are two, 3 and 5. 30 can be written equally a product of its prime factors. The prime factors are written in numerical order. 30 = 2 × 3 × 5

2 of 8

Example 2: A factor tree for twenty-four. This is a diagram of numbers branching from twenty-four. Twenty-four going to eight and a circled three. Eight going to a circled two and to four. Four going to two and two – both circled. — The prime number factors of 24 are 2 and 3

iii of 8

Same diagram with the circled numbers three, and then three twos. To the right: Twenty-four equals two multiplied by two multiplied by two multiplied by three. — The prime factors of 24 are 2 and 3. 24 can exist written every bit a product of its prime factors. The prime factors are written in numerical social club. 24 = 2 x 2 x two x 3

4 of eight

Twenty-four equals two cubed (highlighted) multiplied by three. — 24 equally a product of prime factors can also exist written in index form (with powers). This is considering 2 occurs more than once. 24 = 23 × 3

five of 8

Example 3: A factor tree for seven hundred and fifty. This is a diagram of numbers branching from seven-hundred and fifty. Seven-hundred and fifty going to seventy-five and ten. Seventy-five going to twenty-five and a circled three. Twenty-five going to five and five – both circled. Ten going to two and five – both circled. — The prime factors of 750 are 2, three and 5

6 of viii

Same diagram. Below it: Seven-hundred and fifty equals two multiplied by three multiplied by five multiplied by five multiplied by five. Seven-hundred and fifty equals two multiplied by three multiplied by five cubed. — The prime number factors of 750 are 2, 3 and 5. 750 can be written every bit a production of its prime factors. The prime factors are written in numerical lodge. 750 = 2 x three x 5 x five x 5

7 of 8

All five's in the diagram and the product of prime factors are highlighted. — 750 equally a product of prime factors is 2 ten iii x 5 10 5 x v. This can as well exist written in index form (with powers) as 5 occurs more than once. 750 = 2 × 3 × 5³

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Practice what you've learned virtually finding the factors of a number with this quiz. Yous may need a pen and paper for some of these questions.

Finding factors and gene pairs tin can be useful in many different situations in real life.

For example, a couple are getting married and are planning their wedding. They have 72 guests coming who all need a seat. The tables tin seat upwardly to 12 people.

By using factor pairs , the couple can choose different combinations to suit their friends and family unit:

12 tables of 6 guests
9 tables of 8 guests
eight tables of 9 guests
6 tables of 12 guests

A wedding venue ready for guests to arrive.