What is the Greatest Common Factor of 20142 and 20160?

Greatest common factor (GCF) of 20142 and 20160 is 18.

GCF(20142,20160) = 18

We will now calculate the prime factors of 20142 and 20160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20142 and 20160.

How to find the GCF of 20142 and 20160?

We will first find the prime factorization of 20142 and 20160. After we will calculate the factors of 20142 and 20160 and find the biggest common factor number .

Step-1: Prime Factorization of 20142

Prime factors of 20142 are 2, 3, 373. Prime factorization of 20142 in exponential form is:

20142 = 2¹ × 3³ × 373¹

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 20142

List of positive integer factors of 20142 that divides 20142 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 373, 746, 1119, 2238, 3357, 6714, 10071

Step-4: Factors of 20160

List of positive integer factors of 20160 that divides 20142 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 20142 and 20160. The biggest common factor number is the GCF number.
So the greatest common factor 20142 and 20160 is 18.

Also check out the Least Common Multiple of 20142 and 20160