What is the Greatest Common Factor of 42100 and 42105?

Greatest common factor (GCF) of 42100 and 42105 is 5.

GCF(42100,42105) = 5

We will now calculate the prime factors of 42100 and 42105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42100 and 42105.

How to find the GCF of 42100 and 42105?

We will first find the prime factorization of 42100 and 42105. After we will calculate the factors of 42100 and 42105 and find the biggest common factor number .

Step-1: Prime Factorization of 42100

Prime factors of 42100 are 2, 5, 421. Prime factorization of 42100 in exponential form is:

42100 = 2² × 5² × 421¹

Step-2: Prime Factorization of 42105

Prime factors of 42105 are 3, 5, 7, 401. Prime factorization of 42105 in exponential form is:

42105 = 3¹ × 5¹ × 7¹ × 401¹

Step-3: Factors of 42100

List of positive integer factors of 42100 that divides 42100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 421, 842, 1684, 2105, 4210, 8420, 10525, 21050

Step-4: Factors of 42105

List of positive integer factors of 42105 that divides 42100 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 401, 1203, 2005, 2807, 6015, 8421, 14035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42100 and 42105. The biggest common factor number is the GCF number.
So the greatest common factor 42100 and 42105 is 5.

Also check out the Least Common Multiple of 42100 and 42105