What is the Greatest Common Factor of 7514 and 7532?

Greatest common factor (GCF) of 7514 and 7532 is 2.

GCF(7514,7532) = 2

We will now calculate the prime factors of 7514 and 7532, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7514 and 7532.

How to find the GCF of 7514 and 7532?

We will first find the prime factorization of 7514 and 7532. After we will calculate the factors of 7514 and 7532 and find the biggest common factor number .

Step-1: Prime Factorization of 7514

Prime factors of 7514 are 2, 13, 17. Prime factorization of 7514 in exponential form is:

7514 = 2¹ × 13¹ × 17²

Step-2: Prime Factorization of 7532

Prime factors of 7532 are 2, 7, 269. Prime factorization of 7532 in exponential form is:

7532 = 2² × 7¹ × 269¹

Step-3: Factors of 7514

List of positive integer factors of 7514 that divides 7514 without a remainder.

1, 2, 13, 17, 26, 34, 221, 289, 442, 578, 3757

Step-4: Factors of 7532

List of positive integer factors of 7532 that divides 7514 without a remainder.

1, 2, 4, 7, 14, 28, 269, 538, 1076, 1883, 3766

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7514 and 7532. The biggest common factor number is the GCF number.
So the greatest common factor 7514 and 7532 is 2.

Also check out the Least Common Multiple of 7514 and 7532