What is the Greatest Common Factor of 74137 and 74144?

Greatest common factor (GCF) of 74137 and 74144 is 7.

GCF(74137,74144) = 7

We will now calculate the prime factors of 74137 and 74144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74137 and 74144.

How to find the GCF of 74137 and 74144?

We will first find the prime factorization of 74137 and 74144. After we will calculate the factors of 74137 and 74144 and find the biggest common factor number .

Step-1: Prime Factorization of 74137

Prime factors of 74137 are 7, 17, 89. Prime factorization of 74137 in exponential form is:

74137 = 7² × 17¹ × 89¹

Step-2: Prime Factorization of 74144

Prime factors of 74144 are 2, 7, 331. Prime factorization of 74144 in exponential form is:

74144 = 2⁵ × 7¹ × 331¹

Step-3: Factors of 74137

List of positive integer factors of 74137 that divides 74137 without a remainder.

1, 7, 17, 49, 89, 119, 623, 833, 1513, 4361, 10591

Step-4: Factors of 74144

List of positive integer factors of 74144 that divides 74137 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 331, 662, 1324, 2317, 2648, 4634, 5296, 9268, 10592, 18536, 37072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74137 and 74144. The biggest common factor number is the GCF number.
So the greatest common factor 74137 and 74144 is 7.

Also check out the Least Common Multiple of 74137 and 74144