What is the Greatest Common Factor of 74160 and 74165?

Greatest common factor (GCF) of 74160 and 74165 is 5.

GCF(74160,74165) = 5

We will now calculate the prime factors of 74160 and 74165, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74160 and 74165.

How to find the GCF of 74160 and 74165?

We will first find the prime factorization of 74160 and 74165. After we will calculate the factors of 74160 and 74165 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 74165

Prime factors of 74165 are 5, 7, 13, 163. Prime factorization of 74165 in exponential form is:

74165 = 5¹ × 7¹ × 13¹ × 163¹

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 74165

List of positive integer factors of 74165 that divides 74160 without a remainder.

1, 5, 7, 13, 35, 65, 91, 163, 455, 815, 1141, 2119, 5705, 10595, 14833

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74160 and 74165. The biggest common factor number is the GCF number.
So the greatest common factor 74160 and 74165 is 5.

Also check out the Least Common Multiple of 74160 and 74165