What is the Greatest Common Factor of 42208 and 42214?

Greatest common factor (GCF) of 42208 and 42214 is 2.

GCF(42208,42214) = 2

We will now calculate the prime factors of 42208 and 42214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42208 and 42214.

How to find the GCF of 42208 and 42214?

We will first find the prime factorization of 42208 and 42214. After we will calculate the factors of 42208 and 42214 and find the biggest common factor number .

Step-1: Prime Factorization of 42208

Prime factors of 42208 are 2, 1319. Prime factorization of 42208 in exponential form is:

42208 = 2⁵ × 1319¹

Step-2: Prime Factorization of 42214

Prime factors of 42214 are 2, 21107. Prime factorization of 42214 in exponential form is:

42214 = 2¹ × 21107¹

Step-3: Factors of 42208

List of positive integer factors of 42208 that divides 42208 without a remainder.

1, 2, 4, 8, 16, 32, 1319, 2638, 5276, 10552, 21104

Step-4: Factors of 42214

List of positive integer factors of 42214 that divides 42208 without a remainder.

1, 2, 21107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42208 and 42214. The biggest common factor number is the GCF number.
So the greatest common factor 42208 and 42214 is 2.

Also check out the Least Common Multiple of 42208 and 42214