What is the Greatest Common Factor of 74970 and 74975?

Greatest common factor (GCF) of 74970 and 74975 is 5.

GCF(74970,74975) = 5

We will now calculate the prime factors of 74970 and 74975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74970 and 74975.

How to find the GCF of 74970 and 74975?

We will first find the prime factorization of 74970 and 74975. After we will calculate the factors of 74970 and 74975 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74975

Prime factors of 74975 are 5, 2999. Prime factorization of 74975 in exponential form is:

74975 = 5² × 2999¹

Step-3: Factors of 74970

List of positive integer factors of 74970 that divides 74970 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

Step-4: Factors of 74975

List of positive integer factors of 74975 that divides 74970 without a remainder.

1, 5, 25, 2999, 14995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74970 and 74975. The biggest common factor number is the GCF number.
So the greatest common factor 74970 and 74975 is 5.

Also check out the Least Common Multiple of 74970 and 74975