What is the Greatest Common Factor of 1654 and 1674?

Greatest common factor (GCF) of 1654 and 1674 is 2.

GCF(1654,1674) = 2

We will now calculate the prime factors of 1654 and 1674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1654 and 1674.

How to find the GCF of 1654 and 1674?

We will first find the prime factorization of 1654 and 1674. After we will calculate the factors of 1654 and 1674 and find the biggest common factor number .

Step-1: Prime Factorization of 1654

Prime factors of 1654 are 2, 827. Prime factorization of 1654 in exponential form is:

1654 = 2¹ × 827¹

Step-2: Prime Factorization of 1674

Prime factors of 1674 are 2, 3, 31. Prime factorization of 1674 in exponential form is:

1674 = 2¹ × 3³ × 31¹

Step-3: Factors of 1654

List of positive integer factors of 1654 that divides 1654 without a remainder.

1, 2, 827

Step-4: Factors of 1674

List of positive integer factors of 1674 that divides 1654 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1654 and 1674. The biggest common factor number is the GCF number.
So the greatest common factor 1654 and 1674 is 2.

Also check out the Least Common Multiple of 1654 and 1674