What is the Greatest Common Factor of 67100 and 67114?

Greatest common factor (GCF) of 67100 and 67114 is 2.

GCF(67100,67114) = 2

We will now calculate the prime factors of 67100 and 67114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67100 and 67114.

How to find the GCF of 67100 and 67114?

We will first find the prime factorization of 67100 and 67114. After we will calculate the factors of 67100 and 67114 and find the biggest common factor number .

Step-1: Prime Factorization of 67100

Prime factors of 67100 are 2, 5, 11, 61. Prime factorization of 67100 in exponential form is:

67100 = 2² × 5² × 11¹ × 61¹

Step-2: Prime Factorization of 67114

Prime factors of 67114 are 2, 23, 1459. Prime factorization of 67114 in exponential form is:

67114 = 2¹ × 23¹ × 1459¹

Step-3: Factors of 67100

List of positive integer factors of 67100 that divides 67100 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 61, 100, 110, 122, 220, 244, 275, 305, 550, 610, 671, 1100, 1220, 1342, 1525, 2684, 3050, 3355, 6100, 6710, 13420, 16775, 33550

Step-4: Factors of 67114

List of positive integer factors of 67114 that divides 67100 without a remainder.

1, 2, 23, 46, 1459, 2918, 33557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67100 and 67114. The biggest common factor number is the GCF number.
So the greatest common factor 67100 and 67114 is 2.

Also check out the Least Common Multiple of 67100 and 67114