What is the Greatest Common Factor of 75696 and 75714?

Greatest common factor (GCF) of 75696 and 75714 is 6.

GCF(75696,75714) = 6

We will now calculate the prime factors of 75696 and 75714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75696 and 75714.

How to find the GCF of 75696 and 75714?

We will first find the prime factorization of 75696 and 75714. After we will calculate the factors of 75696 and 75714 and find the biggest common factor number .

Step-1: Prime Factorization of 75696

Prime factors of 75696 are 2, 3, 19, 83. Prime factorization of 75696 in exponential form is:

75696 = 2⁴ × 3¹ × 19¹ × 83¹

Step-2: Prime Factorization of 75714

Prime factors of 75714 are 2, 3, 12619. Prime factorization of 75714 in exponential form is:

75714 = 2¹ × 3¹ × 12619¹

Step-3: Factors of 75696

List of positive integer factors of 75696 that divides 75696 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 83, 114, 152, 166, 228, 249, 304, 332, 456, 498, 664, 912, 996, 1328, 1577, 1992, 3154, 3984, 4731, 6308, 9462, 12616, 18924, 25232, 37848

Step-4: Factors of 75714

List of positive integer factors of 75714 that divides 75696 without a remainder.

1, 2, 3, 6, 12619, 25238, 37857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75696 and 75714. The biggest common factor number is the GCF number.
So the greatest common factor 75696 and 75714 is 6.

Also check out the Least Common Multiple of 75696 and 75714