What is the Greatest Common Factor of 75698 and 75712?

Greatest common factor (GCF) of 75698 and 75712 is 14.

GCF(75698,75712) = 14

We will now calculate the prime factors of 75698 and 75712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75698 and 75712.

How to find the GCF of 75698 and 75712?

We will first find the prime factorization of 75698 and 75712. After we will calculate the factors of 75698 and 75712 and find the biggest common factor number .

Step-1: Prime Factorization of 75698

Prime factors of 75698 are 2, 7, 5407. Prime factorization of 75698 in exponential form is:

75698 = 2¹ × 7¹ × 5407¹

Step-2: 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-3: Factors of 75698

List of positive integer factors of 75698 that divides 75698 without a remainder.

1, 2, 7, 14, 5407, 10814, 37849

Step-4: Factors of 75712

List of positive integer factors of 75712 that divides 75698 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75698 and 75712. The biggest common factor number is the GCF number.
So the greatest common factor 75698 and 75712 is 14.

Also check out the Least Common Multiple of 75698 and 75712