What is the Greatest Common Factor of 20160 and 20169?

Greatest common factor (GCF) of 20160 and 20169 is 9.

GCF(20160,20169) = 9

We will now calculate the prime factors of 20160 and 20169, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20160 and 20169.

How to find the GCF of 20160 and 20169?

We will first find the prime factorization of 20160 and 20169. After we will calculate the factors of 20160 and 20169 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 20169

Prime factors of 20169 are 3, 83. Prime factorization of 20169 in exponential form is:

20169 = 3⁵ × 83¹

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 20169

List of positive integer factors of 20169 that divides 20160 without a remainder.

1, 3, 9, 27, 81, 83, 243, 249, 747, 2241, 6723

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20160 and 20169. The biggest common factor number is the GCF number.
So the greatest common factor 20160 and 20169 is 9.

Also check out the Least Common Multiple of 20160 and 20169