What is the Greatest Common Factor of 20160 and 20175?

Greatest common factor (GCF) of 20160 and 20175 is 15.

GCF(20160,20175) = 15

We will now calculate the prime factors of 20160 and 20175, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20160 and 20175.

How to find the GCF of 20160 and 20175?

We will first find the prime factorization of 20160 and 20175. After we will calculate the factors of 20160 and 20175 and find the biggest common factor number .

Step-1: Prime Factorization of 20160

Prime factors of 20160 are 2, 3, 5, 7. Prime factorization of 20160 in exponential form is:

20160 = 2⁶ × 3² × 5¹ × 7¹

Step-2: Prime Factorization of 20175

Prime factors of 20175 are 3, 5, 269. Prime factorization of 20175 in exponential form is:

20175 = 3¹ × 5² × 269¹

Step-3: Factors of 20160

List of positive integer factors of 20160 that divides 20160 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080

Step-4: Factors of 20175

List of positive integer factors of 20175 that divides 20160 without a remainder.

1, 3, 5, 15, 25, 75, 269, 807, 1345, 4035, 6725

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20160 and 20175. The biggest common factor number is the GCF number.
So the greatest common factor 20160 and 20175 is 15.

Also check out the Least Common Multiple of 20160 and 20175