What is the Greatest Common Factor of 74955 and 74970?

Greatest common factor (GCF) of 74955 and 74970 is 15.

GCF(74955,74970) = 15

We will now calculate the prime factors of 74955 and 74970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74955 and 74970.

How to find the GCF of 74955 and 74970?

We will first find the prime factorization of 74955 and 74970. After we will calculate the factors of 74955 and 74970 and find the biggest common factor number .

Step-1: Prime Factorization of 74955

Prime factors of 74955 are 3, 5, 19, 263. Prime factorization of 74955 in exponential form is:

74955 = 3¹ × 5¹ × 19¹ × 263¹

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 74955

List of positive integer factors of 74955 that divides 74955 without a remainder.

1, 3, 5, 15, 19, 57, 95, 263, 285, 789, 1315, 3945, 4997, 14991, 24985

Step-4: Factors of 74970

List of positive integer factors of 74970 that divides 74955 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 74955 and 74970. The biggest common factor number is the GCF number.
So the greatest common factor 74955 and 74970 is 15.

Also check out the Least Common Multiple of 74955 and 74970