What is the Greatest Common Factor of 20160 and 20172?

Greatest common factor (GCF) of 20160 and 20172 is 12.

GCF(20160,20172) = 12

We will now calculate the prime factors of 20160 and 20172, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20160 and 20172.

How to find the GCF of 20160 and 20172?

We will first find the prime factorization of 20160 and 20172. After we will calculate the factors of 20160 and 20172 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 20172

Prime factors of 20172 are 2, 3, 41. Prime factorization of 20172 in exponential form is:

20172 = 2² × 3¹ × 41²

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 20172

List of positive integer factors of 20172 that divides 20160 without a remainder.

1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492, 1681, 3362, 5043, 6724, 10086

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20160 and 20172. The biggest common factor number is the GCF number.
So the greatest common factor 20160 and 20172 is 12.

Also check out the Least Common Multiple of 20160 and 20172