What is the Greatest Common Factor of 1514 and 1530?

Greatest common factor (GCF) of 1514 and 1530 is 2.

GCF(1514,1530) = 2

We will now calculate the prime factors of 1514 and 1530, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1514 and 1530.

How to find the GCF of 1514 and 1530?

We will first find the prime factorization of 1514 and 1530. After we will calculate the factors of 1514 and 1530 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 1530

Prime factors of 1530 are 2, 3, 5, 17. Prime factorization of 1530 in exponential form is:

1530 = 2¹ × 3² × 5¹ × 17¹

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 1530

List of positive integer factors of 1530 that divides 1514 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1514 and 1530. The biggest common factor number is the GCF number.
So the greatest common factor 1514 and 1530 is 2.

Also check out the Least Common Multiple of 1514 and 1530