What is the Greatest Common Factor of 42105 and 42119?

Greatest common factor (GCF) of 42105 and 42119 is 7.

GCF(42105,42119) = 7

We will now calculate the prime factors of 42105 and 42119, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42105 and 42119.

How to find the GCF of 42105 and 42119?

We will first find the prime factorization of 42105 and 42119. After we will calculate the factors of 42105 and 42119 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 42119

Prime factors of 42119 are 7, 11, 547. Prime factorization of 42119 in exponential form is:

42119 = 7¹ × 11¹ × 547¹

Step-3: Factors of 42105

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

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

Step-4: Factors of 42119

List of positive integer factors of 42119 that divides 42105 without a remainder.

1, 7, 11, 77, 547, 3829, 6017

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42105 and 42119. The biggest common factor number is the GCF number.
So the greatest common factor 42105 and 42119 is 7.

Also check out the Least Common Multiple of 42105 and 42119