What is the Greatest Common Factor of 42164 and 42180?

Greatest common factor (GCF) of 42164 and 42180 is 4.

GCF(42164,42180) = 4

We will now calculate the prime factors of 42164 and 42180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42164 and 42180.

How to find the GCF of 42164 and 42180?

We will first find the prime factorization of 42164 and 42180. After we will calculate the factors of 42164 and 42180 and find the biggest common factor number .

Step-1: Prime Factorization of 42164

Prime factors of 42164 are 2, 83, 127. Prime factorization of 42164 in exponential form is:

42164 = 2² × 83¹ × 127¹

Step-2: Prime Factorization of 42180

Prime factors of 42180 are 2, 3, 5, 19, 37. Prime factorization of 42180 in exponential form is:

42180 = 2² × 3¹ × 5¹ × 19¹ × 37¹

Step-3: Factors of 42164

List of positive integer factors of 42164 that divides 42164 without a remainder.

1, 2, 4, 83, 127, 166, 254, 332, 508, 10541, 21082

Step-4: Factors of 42180

List of positive integer factors of 42180 that divides 42164 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 37, 38, 57, 60, 74, 76, 95, 111, 114, 148, 185, 190, 222, 228, 285, 370, 380, 444, 555, 570, 703, 740, 1110, 1140, 1406, 2109, 2220, 2812, 3515, 4218, 7030, 8436, 10545, 14060, 21090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42164 and 42180. The biggest common factor number is the GCF number.
So the greatest common factor 42164 and 42180 is 4.

Also check out the Least Common Multiple of 42164 and 42180