What is the Greatest Common Factor of 65696 and 65700?

Greatest common factor (GCF) of 65696 and 65700 is 4.

GCF(65696,65700) = 4

We will now calculate the prime factors of 65696 and 65700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65696 and 65700.

How to find the GCF of 65696 and 65700?

We will first find the prime factorization of 65696 and 65700. After we will calculate the factors of 65696 and 65700 and find the biggest common factor number .

Step-1: Prime Factorization of 65696

Prime factors of 65696 are 2, 2053. Prime factorization of 65696 in exponential form is:

65696 = 2⁵ × 2053¹

Step-2: Prime Factorization of 65700

Prime factors of 65700 are 2, 3, 5, 73. Prime factorization of 65700 in exponential form is:

65700 = 2² × 3² × 5² × 73¹

Step-3: Factors of 65696

List of positive integer factors of 65696 that divides 65696 without a remainder.

1, 2, 4, 8, 16, 32, 2053, 4106, 8212, 16424, 32848

Step-4: Factors of 65700

List of positive integer factors of 65700 that divides 65696 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 73, 75, 90, 100, 146, 150, 180, 219, 225, 292, 300, 365, 438, 450, 657, 730, 876, 900, 1095, 1314, 1460, 1825, 2190, 2628, 3285, 3650, 4380, 5475, 6570, 7300, 10950, 13140, 16425, 21900, 32850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65696 and 65700. The biggest common factor number is the GCF number.
So the greatest common factor 65696 and 65700 is 4.

Also check out the Least Common Multiple of 65696 and 65700