What is the Greatest Common Factor of 1506 and 1514?

Greatest common factor (GCF) of 1506 and 1514 is 2.

GCF(1506,1514) = 2

We will now calculate the prime factors of 1506 and 1514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1506 and 1514.

How to find the GCF of 1506 and 1514?

We will first find the prime factorization of 1506 and 1514. After we will calculate the factors of 1506 and 1514 and find the biggest common factor number .

Step-1: Prime Factorization of 1506

Prime factors of 1506 are 2, 3, 251. Prime factorization of 1506 in exponential form is:

1506 = 2¹ × 3¹ × 251¹

Step-2: Prime Factorization of 1514

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

1514 = 2¹ × 757¹

Step-3: Factors of 1506

List of positive integer factors of 1506 that divides 1506 without a remainder.

1, 2, 3, 6, 251, 502, 753

Step-4: Factors of 1514

List of positive integer factors of 1514 that divides 1506 without a remainder.

1, 2, 757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1506 and 1514. The biggest common factor number is the GCF number.
So the greatest common factor 1506 and 1514 is 2.

Also check out the Least Common Multiple of 1506 and 1514