What is the Greatest Common Factor of 74160 and 74175?

Greatest common factor (GCF) of 74160 and 74175 is 15.

GCF(74160,74175) = 15

We will now calculate the prime factors of 74160 and 74175, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74160 and 74175.

How to find the GCF of 74160 and 74175?

We will first find the prime factorization of 74160 and 74175. After we will calculate the factors of 74160 and 74175 and find the biggest common factor number .

Step-1: Prime Factorization of 74160

Prime factors of 74160 are 2, 3, 5, 103. Prime factorization of 74160 in exponential form is:

74160 = 2⁴ × 3² × 5¹ × 103¹

Step-2: Prime Factorization of 74175

Prime factors of 74175 are 3, 5, 23, 43. Prime factorization of 74175 in exponential form is:

74175 = 3¹ × 5² × 23¹ × 43¹

Step-3: Factors of 74160

List of positive integer factors of 74160 that divides 74160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 103, 120, 144, 180, 206, 240, 309, 360, 412, 515, 618, 720, 824, 927, 1030, 1236, 1545, 1648, 1854, 2060, 2472, 3090, 3708, 4120, 4635, 4944, 6180, 7416, 8240, 9270, 12360, 14832, 18540, 24720, 37080

Step-4: Factors of 74175

List of positive integer factors of 74175 that divides 74160 without a remainder.

1, 3, 5, 15, 23, 25, 43, 69, 75, 115, 129, 215, 345, 575, 645, 989, 1075, 1725, 2967, 3225, 4945, 14835, 24725

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74160 and 74175. The biggest common factor number is the GCF number.
So the greatest common factor 74160 and 74175 is 15.

Also check out the Least Common Multiple of 74160 and 74175