What is the Greatest Common Factor of 1514 and 1524?

Greatest common factor (GCF) of 1514 and 1524 is 2.

GCF(1514,1524) = 2

We will now calculate the prime factors of 1514 and 1524, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1514 and 1524.

How to find the GCF of 1514 and 1524?

We will first find the prime factorization of 1514 and 1524. After we will calculate the factors of 1514 and 1524 and find the biggest common factor number .

Step-1: Prime Factorization of 1514

Prime factors of 1514 are 2, 757. Prime factorization of 1514 in exponential form is:

1514 = 2¹ × 757¹

Step-2: Prime Factorization of 1524

Prime factors of 1524 are 2, 3, 127. Prime factorization of 1524 in exponential form is:

1524 = 2² × 3¹ × 127¹

Step-3: Factors of 1514

List of positive integer factors of 1514 that divides 1514 without a remainder.

1, 2, 757

Step-4: Factors of 1524

List of positive integer factors of 1524 that divides 1514 without a remainder.

1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1514 and 1524. The biggest common factor number is the GCF number.
So the greatest common factor 1514 and 1524 is 2.

Also check out the Least Common Multiple of 1514 and 1524