What is the Greatest Common Factor of 75712 and 75730?

Greatest common factor (GCF) of 75712 and 75730 is 2.

GCF(75712,75730) = 2

We will now calculate the prime factors of 75712 and 75730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75712 and 75730.

How to find the GCF of 75712 and 75730?

We will first find the prime factorization of 75712 and 75730. After we will calculate the factors of 75712 and 75730 and find the biggest common factor number .

Step-1: Prime Factorization of 75712

Prime factors of 75712 are 2, 7, 13. Prime factorization of 75712 in exponential form is:

75712 = 2⁶ × 7¹ × 13²

Step-2: Prime Factorization of 75730

Prime factors of 75730 are 2, 5, 7573. Prime factorization of 75730 in exponential form is:

75730 = 2¹ × 5¹ × 7573¹

Step-3: Factors of 75712

List of positive integer factors of 75712 that divides 75712 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 448, 676, 728, 832, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 5824, 9464, 10816, 18928, 37856

Step-4: Factors of 75730

List of positive integer factors of 75730 that divides 75712 without a remainder.

1, 2, 5, 10, 7573, 15146, 37865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75712 and 75730. The biggest common factor number is the GCF number.
So the greatest common factor 75712 and 75730 is 2.

Also check out the Least Common Multiple of 75712 and 75730