What is the Greatest Common Factor of 67858 and 67872?

Greatest common factor (GCF) of 67858 and 67872 is 14.

GCF(67858,67872) = 14

We will now calculate the prime factors of 67858 and 67872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67858 and 67872.

How to find the GCF of 67858 and 67872?

We will first find the prime factorization of 67858 and 67872. After we will calculate the factors of 67858 and 67872 and find the biggest common factor number .

Step-1: Prime Factorization of 67858

Prime factors of 67858 are 2, 7, 37, 131. Prime factorization of 67858 in exponential form is:

67858 = 2¹ × 7¹ × 37¹ × 131¹

Step-2: 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-3: Factors of 67858

List of positive integer factors of 67858 that divides 67858 without a remainder.

1, 2, 7, 14, 37, 74, 131, 259, 262, 518, 917, 1834, 4847, 9694, 33929

Step-4: Factors of 67872

List of positive integer factors of 67872 that divides 67858 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67858 and 67872. The biggest common factor number is the GCF number.
So the greatest common factor 67858 and 67872 is 14.

Also check out the Least Common Multiple of 67858 and 67872