Question

find the h.c.f of 124, 216 using the long division​

Answer 1

This algorithm involves the operation of dividing and calculating remainders.

'a' and 'b' are the two positive integers, 'a' >= 'b'.

Divide 'a' by 'b' and get the remainder, 'r'.

If 'r' = 0, STOP. 'b' = the GCF (HCF, GCD) of 'a' and 'b'.

Else: Replace ('a' by 'b') & ('b' by 'r'). Return to the division step above.



Step 1. Divide the larger number by the smaller one:
216 ÷ 124 = 1 + 92;
Step 2. Divide the smaller number by the above operation's remainder:
124 ÷ 92 = 1 + 32;
Step 3. Divide the remainder from the step 1 by the remainder from the step 2:
92 ÷ 32 = 2 + 28;
Step 4. Divide the remainder from the step 2 by the remainder from the step 3:
32 ÷ 28 = 1 + 4;
Step 5. Divide the remainder from the step 3 by the remainder from the step 4:
28 ÷ 4 = 7 + 0;
At this step, the remainder is zero, so we stop:
4 is the number we were looking for, the last remainder that is not zero.
This is the greatest common factor (divisor).

Greatest (highest) common factor (divisor):
gcf, hcf, gcd (216; 124) = 4

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