What is the Greatest Common Factor of 1857 and 1872?

Greatest common factor (GCF) of 1857 and 1872 is 3.

GCF(1857,1872) = 3

We will now calculate the prime factors of 1857 and 1872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1857 and 1872.

How to find the GCF of 1857 and 1872?

We will first find the prime factorization of 1857 and 1872. After we will calculate the factors of 1857 and 1872 and find the biggest common factor number .

Step-1: Prime Factorization of 1857

Prime factors of 1857 are 3, 619. Prime factorization of 1857 in exponential form is:

1857 = 3¹ × 619¹

Step-2: Prime Factorization of 1872

Prime factors of 1872 are 2, 3, 13. Prime factorization of 1872 in exponential form is:

1872 = 2⁴ × 3² × 13¹

Step-3: Factors of 1857

List of positive integer factors of 1857 that divides 1857 without a remainder.

1, 3, 619

Step-4: Factors of 1872

List of positive integer factors of 1872 that divides 1857 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1857 and 1872. The biggest common factor number is the GCF number.
So the greatest common factor 1857 and 1872 is 3.

Also check out the Least Common Multiple of 1857 and 1872