What is the Greatest Common Factor of 1872 and 1888?

Greatest common factor (GCF) of 1872 and 1888 is 16.

GCF(1872,1888) = 16

We will now calculate the prime factors of 1872 and 1888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1872 and 1888.

How to find the GCF of 1872 and 1888?

We will first find the prime factorization of 1872 and 1888. After we will calculate the factors of 1872 and 1888 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1888

Prime factors of 1888 are 2, 59. Prime factorization of 1888 in exponential form is:

1888 = 2⁵ × 59¹

Step-3: Factors of 1872

List of positive integer factors of 1872 that divides 1872 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

Step-4: Factors of 1888

List of positive integer factors of 1888 that divides 1872 without a remainder.

1, 2, 4, 8, 16, 32, 59, 118, 236, 472, 944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1872 and 1888. The biggest common factor number is the GCF number.
So the greatest common factor 1872 and 1888 is 16.

Also check out the Least Common Multiple of 1872 and 1888