What is the Greatest Common Factor of 70140 and 70149?

Greatest common factor (GCF) of 70140 and 70149 is 3.

GCF(70140,70149) = 3

We will now calculate the prime factors of 70140 and 70149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70140 and 70149.

How to find the GCF of 70140 and 70149?

We will first find the prime factorization of 70140 and 70149. After we will calculate the factors of 70140 and 70149 and find the biggest common factor number .

Step-1: Prime Factorization of 70140

Prime factors of 70140 are 2, 3, 5, 7, 167. Prime factorization of 70140 in exponential form is:

70140 = 2² × 3¹ × 5¹ × 7¹ × 167¹

Step-2: Prime Factorization of 70149

Prime factors of 70149 are 3, 67, 349. Prime factorization of 70149 in exponential form is:

70149 = 3¹ × 67¹ × 349¹

Step-3: Factors of 70140

List of positive integer factors of 70140 that divides 70140 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 167, 210, 334, 420, 501, 668, 835, 1002, 1169, 1670, 2004, 2338, 2505, 3340, 3507, 4676, 5010, 5845, 7014, 10020, 11690, 14028, 17535, 23380, 35070

Step-4: Factors of 70149

List of positive integer factors of 70149 that divides 70140 without a remainder.

1, 3, 67, 201, 349, 1047, 23383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70140 and 70149. The biggest common factor number is the GCF number.
So the greatest common factor 70140 and 70149 is 3.

Also check out the Least Common Multiple of 70140 and 70149