What is the Greatest Common Factor of 20144 and 20160?

Greatest common factor (GCF) of 20144 and 20160 is 16.

GCF(20144,20160) = 16

We will now calculate the prime factors of 20144 and 20160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20144 and 20160.

How to find the GCF of 20144 and 20160?

We will first find the prime factorization of 20144 and 20160. After we will calculate the factors of 20144 and 20160 and find the biggest common factor number .

Step-1: Prime Factorization of 20144

Prime factors of 20144 are 2, 1259. Prime factorization of 20144 in exponential form is:

20144 = 2⁴ × 1259¹

Step-2: 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-3: Factors of 20144

List of positive integer factors of 20144 that divides 20144 without a remainder.

1, 2, 4, 8, 16, 1259, 2518, 5036, 10072

Step-4: Factors of 20160

List of positive integer factors of 20160 that divides 20144 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20144 and 20160. The biggest common factor number is the GCF number.
So the greatest common factor 20144 and 20160 is 16.

Also check out the Least Common Multiple of 20144 and 20160