What is the Greatest Common Factor of 74142 and 74160?

Greatest common factor (GCF) of 74142 and 74160 is 18.

GCF(74142,74160) = 18

We will now calculate the prime factors of 74142 and 74160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74142 and 74160.

How to find the GCF of 74142 and 74160?

We will first find the prime factorization of 74142 and 74160. After we will calculate the factors of 74142 and 74160 and find the biggest common factor number .

Step-1: Prime Factorization of 74142

Prime factors of 74142 are 2, 3, 1373. Prime factorization of 74142 in exponential form is:

74142 = 2¹ × 3³ × 1373¹

Step-2: 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-3: Factors of 74142

List of positive integer factors of 74142 that divides 74142 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 1373, 2746, 4119, 8238, 12357, 24714, 37071

Step-4: Factors of 74160

List of positive integer factors of 74160 that divides 74142 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74142 and 74160. The biggest common factor number is the GCF number.
So the greatest common factor 74142 and 74160 is 18.

Also check out the Least Common Multiple of 74142 and 74160