What is the Greatest Common Factor of 20160 and 20170?

Greatest common factor (GCF) of 20160 and 20170 is 10.

GCF(20160,20170) = 10

We will now calculate the prime factors of 20160 and 20170, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20160 and 20170.

How to find the GCF of 20160 and 20170?

We will first find the prime factorization of 20160 and 20170. After we will calculate the factors of 20160 and 20170 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 20170

Prime factors of 20170 are 2, 5, 2017. Prime factorization of 20170 in exponential form is:

20170 = 2¹ × 5¹ × 2017¹

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 20170

List of positive integer factors of 20170 that divides 20160 without a remainder.

1, 2, 5, 10, 2017, 4034, 10085

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20160 and 20170. The biggest common factor number is the GCF number.
So the greatest common factor 20160 and 20170 is 10.

Also check out the Least Common Multiple of 20160 and 20170