What is the Greatest Common Factor of 67872 and 67888?

Greatest common factor (GCF) of 67872 and 67888 is 16.

GCF(67872,67888) = 16

We will now calculate the prime factors of 67872 and 67888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67872 and 67888.

How to find the GCF of 67872 and 67888?

We will first find the prime factorization of 67872 and 67888. After we will calculate the factors of 67872 and 67888 and find the biggest common factor number .

Step-1: Prime Factorization of 67872

Prime factors of 67872 are 2, 3, 7, 101. Prime factorization of 67872 in exponential form is:

67872 = 2⁵ × 3¹ × 7¹ × 101¹

Step-2: Prime Factorization of 67888

Prime factors of 67888 are 2, 4243. Prime factorization of 67888 in exponential form is:

67888 = 2⁴ × 4243¹

Step-3: Factors of 67872

List of positive integer factors of 67872 that divides 67872 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 101, 112, 168, 202, 224, 303, 336, 404, 606, 672, 707, 808, 1212, 1414, 1616, 2121, 2424, 2828, 3232, 4242, 4848, 5656, 8484, 9696, 11312, 16968, 22624, 33936

Step-4: Factors of 67888

List of positive integer factors of 67888 that divides 67872 without a remainder.

1, 2, 4, 8, 16, 4243, 8486, 16972, 33944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67872 and 67888. The biggest common factor number is the GCF number.
So the greatest common factor 67872 and 67888 is 16.

Also check out the Least Common Multiple of 67872 and 67888