What is the Greatest Common Factor of 75922 and 75936?

Greatest common factor (GCF) of 75922 and 75936 is 14.

GCF(75922,75936) = 14

We will now calculate the prime factors of 75922 and 75936, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75922 and 75936.

How to find the GCF of 75922 and 75936?

We will first find the prime factorization of 75922 and 75936. After we will calculate the factors of 75922 and 75936 and find the biggest common factor number .

Step-1: Prime Factorization of 75922

Prime factors of 75922 are 2, 7, 11, 17, 29. Prime factorization of 75922 in exponential form is:

75922 = 2¹ × 7¹ × 11¹ × 17¹ × 29¹

Step-2: Prime Factorization of 75936

Prime factors of 75936 are 2, 3, 7, 113. Prime factorization of 75936 in exponential form is:

75936 = 2⁵ × 3¹ × 7¹ × 113¹

Step-3: Factors of 75922

List of positive integer factors of 75922 that divides 75922 without a remainder.

1, 2, 7, 11, 14, 17, 22, 29, 34, 58, 77, 119, 154, 187, 203, 238, 319, 374, 406, 493, 638, 986, 1309, 2233, 2618, 3451, 4466, 5423, 6902, 10846, 37961

Step-4: Factors of 75936

List of positive integer factors of 75936 that divides 75922 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 113, 168, 224, 226, 336, 339, 452, 672, 678, 791, 904, 1356, 1582, 1808, 2373, 2712, 3164, 3616, 4746, 5424, 6328, 9492, 10848, 12656, 18984, 25312, 37968

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75922 and 75936. The biggest common factor number is the GCF number.
So the greatest common factor 75922 and 75936 is 14.

Also check out the Least Common Multiple of 75922 and 75936