What is the Greatest Common Factor of 76944 and 76960?

Greatest common factor (GCF) of 76944 and 76960 is 16.

GCF(76944,76960) = 16

We will now calculate the prime factors of 76944 and 76960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76944 and 76960.

How to find the GCF of 76944 and 76960?

We will first find the prime factorization of 76944 and 76960. After we will calculate the factors of 76944 and 76960 and find the biggest common factor number .

Step-1: Prime Factorization of 76944

Prime factors of 76944 are 2, 3, 7, 229. Prime factorization of 76944 in exponential form is:

76944 = 2⁴ × 3¹ × 7¹ × 229¹

Step-2: Prime Factorization of 76960

Prime factors of 76960 are 2, 5, 13, 37. Prime factorization of 76960 in exponential form is:

76960 = 2⁵ × 5¹ × 13¹ × 37¹

Step-3: Factors of 76944

List of positive integer factors of 76944 that divides 76944 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 229, 336, 458, 687, 916, 1374, 1603, 1832, 2748, 3206, 3664, 4809, 5496, 6412, 9618, 10992, 12824, 19236, 25648, 38472

Step-4: Factors of 76960

List of positive integer factors of 76960 that divides 76944 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 37, 40, 52, 65, 74, 80, 104, 130, 148, 160, 185, 208, 260, 296, 370, 416, 481, 520, 592, 740, 962, 1040, 1184, 1480, 1924, 2080, 2405, 2960, 3848, 4810, 5920, 7696, 9620, 15392, 19240, 38480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76944 and 76960. The biggest common factor number is the GCF number.
So the greatest common factor 76944 and 76960 is 16.

Also check out the Least Common Multiple of 76944 and 76960