What is the Greatest Common Factor of 7138 and 7152?

Greatest common factor (GCF) of 7138 and 7152 is 2.

GCF(7138,7152) = 2

We will now calculate the prime factors of 7138 and 7152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7138 and 7152.

How to find the GCF of 7138 and 7152?

We will first find the prime factorization of 7138 and 7152. After we will calculate the factors of 7138 and 7152 and find the biggest common factor number .

Step-1: Prime Factorization of 7138

Prime factors of 7138 are 2, 43, 83. Prime factorization of 7138 in exponential form is:

7138 = 2¹ × 43¹ × 83¹

Step-2: Prime Factorization of 7152

Prime factors of 7152 are 2, 3, 149. Prime factorization of 7152 in exponential form is:

7152 = 2⁴ × 3¹ × 149¹

Step-3: Factors of 7138

List of positive integer factors of 7138 that divides 7138 without a remainder.

1, 2, 43, 83, 86, 166, 3569

Step-4: Factors of 7152

List of positive integer factors of 7152 that divides 7138 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 149, 298, 447, 596, 894, 1192, 1788, 2384, 3576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7138 and 7152. The biggest common factor number is the GCF number.
So the greatest common factor 7138 and 7152 is 2.

Also check out the Least Common Multiple of 7138 and 7152