GCF of 65 and 100
2026-02-28 10:05 Diff
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Find the GCF of 65 and 100 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number

Here, divide 100 by 65 100 ÷ 65 = 1 (quotient)

The remainder is calculated as 100 - (65×1) = 35

The remainder is 35, not zero, so continue the process

Step 2: Now divide the previous divisor (65) by the previous remainder (35)

Divide 65 by 35 65 ÷ 35 = 1 (quotient), remainder = 65 - (35×1) = 30

The remainder is 30, not zero, so continue the process

Step 3: Now divide the previous divisor (35) by the previous remainder (30)

Divide 35 by 30 35 ÷ 30 = 1 (quotient), remainder = 35 - (30×1) = 5

The remainder is 5, which is not zero, so continue the process

Step 4: Now divide the previous divisor (30) by the remainder (5)

Divide 30 by 5 30 ÷ 5 = 6 (quotient), remainder = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 65 and 100 is 5.