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\\February 16, 2024 2:20 PM Surender Prajapati Proof 5 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.

division method

To find the HCF of two or more numbers by using division method, we follow the following

steps.
Step 1: If there are two given numbers, first identify the larger and the smaller numbers.
Step 2: Take the larger number as dividend and smaller number as divisor and find the
quotient and remainder.

Step 3: Now, take the remainder as new divisor and previous divisor as a new dividend,
and again find the quotient and remainder as we did in previous steps.

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 HCF of any two among given numbers
and then take the third number as dividend and the HCF which we found in earlier as
divisor. Repeat the same process as we did earlier 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 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 HCF of 24 and 396.
– 72 24 396 16
0
– 384

12 24 2
– 24
0
Thus, HCF of 252 and 594 is 18. HCF of 24 and 396 is 12.

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

70 Mathematics-5