What is the Greatest Common Factor of 74956 and 74970?

Greatest common factor (GCF) of 74956 and 74970 is 14.

GCF(74956,74970) = 14

We will now calculate the prime factors of 74956 and 74970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74956 and 74970.

How to find the GCF of 74956 and 74970?

We will first find the prime factorization of 74956 and 74970. After we will calculate the factors of 74956 and 74970 and find the biggest common factor number .

Step-1: Prime Factorization of 74956

Prime factors of 74956 are 2, 7, 2677. Prime factorization of 74956 in exponential form is:

74956 = 2² × 7¹ × 2677¹

Step-2: Prime Factorization of 74970

Prime factors of 74970 are 2, 3, 5, 7, 17. Prime factorization of 74970 in exponential form is:

74970 = 2¹ × 3² × 5¹ × 7² × 17¹

Step-3: Factors of 74956

List of positive integer factors of 74956 that divides 74956 without a remainder.

1, 2, 4, 7, 14, 28, 2677, 5354, 10708, 18739, 37478

Step-4: Factors of 74970

List of positive integer factors of 74970 that divides 74956 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 17, 18, 21, 30, 34, 35, 42, 45, 49, 51, 63, 70, 85, 90, 98, 102, 105, 119, 126, 147, 153, 170, 210, 238, 245, 255, 294, 306, 315, 357, 441, 490, 510, 595, 630, 714, 735, 765, 833, 882, 1071, 1190, 1470, 1530, 1666, 1785, 2142, 2205, 2499, 3570, 4165, 4410, 4998, 5355, 7497, 8330, 10710, 12495, 14994, 24990, 37485

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74956 and 74970. The biggest common factor number is the GCF number.
So the greatest common factor 74956 and 74970 is 14.

Also check out the Least Common Multiple of 74956 and 74970