What is the Greatest Common Factor of 75674 and 75680?

Greatest common factor (GCF) of 75674 and 75680 is 2.

GCF(75674,75680) = 2

We will now calculate the prime factors of 75674 and 75680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75674 and 75680.

How to find the GCF of 75674 and 75680?

We will first find the prime factorization of 75674 and 75680. After we will calculate the factors of 75674 and 75680 and find the biggest common factor number .

Step-1: Prime Factorization of 75674

Prime factors of 75674 are 2, 157, 241. Prime factorization of 75674 in exponential form is:

75674 = 2¹ × 157¹ × 241¹

Step-2: Prime Factorization of 75680

Prime factors of 75680 are 2, 5, 11, 43. Prime factorization of 75680 in exponential form is:

75680 = 2⁵ × 5¹ × 11¹ × 43¹

Step-3: Factors of 75674

List of positive integer factors of 75674 that divides 75674 without a remainder.

1, 2, 157, 241, 314, 482, 37837

Step-4: Factors of 75680

List of positive integer factors of 75680 that divides 75674 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 43, 44, 55, 80, 86, 88, 110, 160, 172, 176, 215, 220, 344, 352, 430, 440, 473, 688, 860, 880, 946, 1376, 1720, 1760, 1892, 2365, 3440, 3784, 4730, 6880, 7568, 9460, 15136, 18920, 37840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75674 and 75680. The biggest common factor number is the GCF number.
So the greatest common factor 75674 and 75680 is 2.

Also check out the Least Common Multiple of 75674 and 75680