What is the Greatest Common Factor of 70105 and 70119?

Greatest common factor (GCF) of 70105 and 70119 is 7.

GCF(70105,70119) = 7

We will now calculate the prime factors of 70105 and 70119, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70105 and 70119.

How to find the GCF of 70105 and 70119?

We will first find the prime factorization of 70105 and 70119. After we will calculate the factors of 70105 and 70119 and find the biggest common factor number .

Step-1: Prime Factorization of 70105

Prime factors of 70105 are 5, 7, 2003. Prime factorization of 70105 in exponential form is:

70105 = 5¹ × 7¹ × 2003¹

Step-2: Prime Factorization of 70119

Prime factors of 70119 are 3, 7, 53. Prime factorization of 70119 in exponential form is:

70119 = 3³ × 7² × 53¹

Step-3: Factors of 70105

List of positive integer factors of 70105 that divides 70105 without a remainder.

1, 5, 7, 35, 2003, 10015, 14021

Step-4: Factors of 70119

List of positive integer factors of 70119 that divides 70105 without a remainder.

1, 3, 7, 9, 21, 27, 49, 53, 63, 147, 159, 189, 371, 441, 477, 1113, 1323, 1431, 2597, 3339, 7791, 10017, 23373

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70105 and 70119. The biggest common factor number is the GCF number.
So the greatest common factor 70105 and 70119 is 7.

Also check out the Least Common Multiple of 70105 and 70119