What is the Greatest Common Factor of 1514 and 1534?

Greatest common factor (GCF) of 1514 and 1534 is 2.

GCF(1514,1534) = 2

We will now calculate the prime factors of 1514 and 1534, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1514 and 1534.

How to find the GCF of 1514 and 1534?

We will first find the prime factorization of 1514 and 1534. After we will calculate the factors of 1514 and 1534 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 1534

Prime factors of 1534 are 2, 13, 59. Prime factorization of 1534 in exponential form is:

1534 = 2¹ × 13¹ × 59¹

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 1534

List of positive integer factors of 1534 that divides 1514 without a remainder.

1, 2, 13, 26, 59, 118, 767

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1514 and 1534. The biggest common factor number is the GCF number.
So the greatest common factor 1514 and 1534 is 2.

Also check out the Least Common Multiple of 1514 and 1534