What is the Greatest Common Factor of 74544 and 74564?

Greatest common factor (GCF) of 74544 and 74564 is 4.

GCF(74544,74564) = 4

We will now calculate the prime factors of 74544 and 74564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74544 and 74564.

How to find the GCF of 74544 and 74564?

We will first find the prime factorization of 74544 and 74564. After we will calculate the factors of 74544 and 74564 and find the biggest common factor number .

Step-1: Prime Factorization of 74544

Prime factors of 74544 are 2, 3, 1553. Prime factorization of 74544 in exponential form is:

74544 = 2⁴ × 3¹ × 1553¹

Step-2: Prime Factorization of 74564

Prime factors of 74564 are 2, 7, 2663. Prime factorization of 74564 in exponential form is:

74564 = 2² × 7¹ × 2663¹

Step-3: Factors of 74544

List of positive integer factors of 74544 that divides 74544 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1553, 3106, 4659, 6212, 9318, 12424, 18636, 24848, 37272

Step-4: Factors of 74564

List of positive integer factors of 74564 that divides 74544 without a remainder.

1, 2, 4, 7, 14, 28, 2663, 5326, 10652, 18641, 37282

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74544 and 74564. The biggest common factor number is the GCF number.
So the greatest common factor 74544 and 74564 is 4.

Also check out the Least Common Multiple of 74544 and 74564