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Common Division Method

To find the HCF of the given numbers by using common division method, we follow these steps.

Step 1: Write the given numbers in a horizontal line, separating them by commas.

Step 2: Divide the numbers by smallest common prime numbers which exactly divides all
the given numbers.

Step 3: Write the quotient directly below the numbers in the next row.

Step 4: Repeat the process of steps 2 and 3, till we get a common divisor for all the numbers.
Step 5: Multiply all the common prime divisors.

The product obtained is the HCF of the given numbers.

Example 3: Find the HCF of 70, 105 and 175 by common division method.
Solution: 5 70, 105,175 The least common prime divisor is 5.

7 14, 21, 35 The least common prime divisor is 7.
2, 3, 5 There is no common prime divisor.

Common factors of 70, 105 and 175 are 5 and 7.

Thus, the HCF of 70, 105 and 175 = 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. It 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, it is the required HCF of more than two numbers.
Example 4: Find the HCF of the following numbers by division method.

(a) 594 and 252

(b) 144, 312 and 396

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