# Multiplication and Division

In Year 5, pupils should be taught about the following key concepts. Here we define and explain these new multiplication and division concepts.

A.Factoring Numbers.

"Factors" are the numbers we multiply to get another number. For instance, factors of 15 are 3 and 5, because 3×5 = 15. Some numbers have more than 1 factorization for example factors of 12 are 1 and 12 they make 1 × 12=12,2 and 6 they make 2× 6=12 ,3 and 4 they make 3×4=12. Factors of 16 are 1 and 16 they make 1 × 16=16 and 2 and 8 they make 2× 8=16, 4 and 4 they make 4×4=16. While factors of 13 are 1 and 13, they make 1×13=13.

Factors can also be defined as any numbers that divide into it exactly. This includes 1 and the number itself. All those numbers that can only be factored 1 times by itself like 13 are called Prime Numbers. Some early prime numbers are 2,3,5,7,11 etc. All other numbers are called Composite Numbers. 1 is a special numbers it is considered not as prime number. Learn from a video below about how to find the factors of a given number. (This video is by Khan Academy.)

B.Common Factors of two numbers

Lets take two numbers.e.g 8 and 18. Factors of 8 are 1,2,4,8 while factors of 18 are 1,2,3,6,9,18. Common factors between these two sets are 1,2,18. Example No 2. Take two other numbers e.g. 24 and 40. Factors of 24 are 1,2,3,4,6,8,12,24 where as factors of 40 are 1,2,4,5,8,10,20,40. Common factors of these two numbers are 1,2,4,8.

C.Highest Common Factor.i.e. H.C.F

The highest number among these common factors is called Highest Common Factor.i.e. H.C.F. In this case 8 is H.C.F of 24 and 40.

D.Prime factors

Prime factors are any factors of a number that are, themselves, prime numbers. There are different methods to find the prime factors of the numbers. The most common method of finding the prime factors is called Prime Factor Tree.

• Prime factors of any number are represented in the form of product and is called Product of Prime factors. E.G. Prime factors of 40 can be calculated as written below.
• ```                  40
/    \
2     20
/   \
2    10
/  \
2    5

40 = 2 x 2 x 2 x 5                                                 ```

Our Worksheets related to Multiplication and Division for Year 5 are available here.