What is the Greatest Common Factor of 1653 and 1672?

Greatest common factor (GCF) of 1653 and 1672 is 19.

GCF(1653,1672) = 19

We will now calculate the prime factors of 1653 and 1672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1653 and 1672.

How to find the GCF of 1653 and 1672?

We will first find the prime factorization of 1653 and 1672. After we will calculate the factors of 1653 and 1672 and find the biggest common factor number .

Step-1: Prime Factorization of 1653

Prime factors of 1653 are 3, 19, 29. Prime factorization of 1653 in exponential form is:

1653 = 3¹ × 19¹ × 29¹

Step-2: Prime Factorization of 1672

Prime factors of 1672 are 2, 11, 19. Prime factorization of 1672 in exponential form is:

1672 = 2³ × 11¹ × 19¹

Step-3: Factors of 1653

List of positive integer factors of 1653 that divides 1653 without a remainder.

1, 3, 19, 29, 57, 87, 551

Step-4: Factors of 1672

List of positive integer factors of 1672 that divides 1653 without a remainder.

1, 2, 4, 8, 11, 19, 22, 38, 44, 76, 88, 152, 209, 418, 836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1653 and 1672. The biggest common factor number is the GCF number.
So the greatest common factor 1653 and 1672 is 19.

Also check out the Least Common Multiple of 1653 and 1672