Question

CLASS V Chapter 6. Date 12.05.2020

MATHS FACTORS AND MULTIPLES

Children, last week we learned about prime and composite numbers, twin primes, perfect numbers and above

all, factors, common factors and two method for factorising numbers (tree method and short division method).

This week we will learn about HCF (Highest Common Factor) and the methods for finding it. As the name

suggests, HCF is the greatest or highest among the common factors of two or more numbers.

There are different methods for finding HCF of two or more numbers.

FIRST METHOD (FACTORISATION METHOD) 16 24

Find the HCF of 16 and 24 1x16= 16 1x24=24

2 x 8=16 2x12=24

Factors of 16 - 1, 2, 4, 8, 16 4x 4=16 3x8 =24

Factors of 24 - 1, 2, 3, 4, 6, 8, 12, 24 4x6 =24

Common factors - 1, 2, 4, and 8 (these nos. are the factors of both 16 and 24 )

HCF - 8 ( greatest among the common factors )

In this method we just write the highest among the common factors.

SECOND METHOD (PRIME FACTORISATION METHOD)

Find the HCF of 18 and 42

2 18 2 42

3 9 3 21

3 3 7 7

1 1

18 = 2 x 3 x 3

KERALA SR SEC SCHOOL, VIKASPURI, NEW DELHI

42 = 2 x 3 x 7

Common factors = 2 & 3 (they are factors of both 18 and 42 )

HCF = 2 x 3 = 6

In this method we multiply the common factors.

THIRD METHOD (LONG DIVISION)

This method is ideal for finding the HCF of large numbers. But here we will take 2 small numbers so that

you may understand better.

Find the HCF of 16 and 20 by long division method.

Step 1 Divide the bigger number 20 by the smaller number 16

1

16 2 0

1 6

4

Now, take the remainder 4 as the divisor and 16 as the new dividend and continue dividing .

1

16 2 0

1 6 4

4 1 6

1 6

0

The remainder is 0 so the HCF of 16 and 20 = 4 (the last divisor)​

Answer 1

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Answer 2

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