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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

Common factors of 27 and 63 are 3 Common factors of 70, 105 and 175 are 5
and 3. Thus, the HCF of 27 and 63 and 7. Thus, the HCF of 70, 105 and 175 =
= 3 × 3 = 9. 5 × 7 = 35.

long division Method

To find the HCF of two or more numbers using the division method, we follow these steps.
Step 1: If there are two given numbers, first identify the greater and the smaller numbers.

Step 2: Take the greater number as the dividend and the smaller number as the divisor
and find the quotient and remainder.

Step 3: Now, take the remainder as the new divisor and the previous divisor as the new
dividend, and again find the quotient and remainder.
Step 4: Repeat the process till the remainder so obtained is zero. The last divisor for which

the remainder is zero is the required HCF of the given two numbers.
Step 5: If there are more than two numbers, we find the HCF of any two of the given numbers

and then take the third number as the dividend and the HCF which we found earlier
as the divisor. Repeat the same process till the remainder is zero.
Hence, the last divisor is the required HCF of more than two numbers.

example 3: Find the HCF of the following numbers by the long division method:

( a) 594 and 252 (b) 144, 312 and 396

Solution:
( a) HCF of 594 and 252. (b) First find the HCF of 144 and 312.

252 594 2 144 312 2
– 504 – 288

90 252 2 24 144 6
– 180 – 144
72 90 1 0
– 72 HCF of 144 and 312 = 24

18 72 4 Now, we find the HCF of 24 and 396.
– 72 24 396 16
0
– 384
12 24 2

– 24
0
Thus, the HCF of 252 and 594 is 18. HCF of 24 and 396 = 12

Thus, the HCF of 144, 312 and 396 is 12.

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