What is the Greatest Common Factor of 46208 and 46214?

Greatest common factor (GCF) of 46208 and 46214 is 2.

GCF(46208,46214) = 2

We will now calculate the prime factors of 46208 and 46214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46208 and 46214.

How to find the GCF of 46208 and 46214?

We will first find the prime factorization of 46208 and 46214. After we will calculate the factors of 46208 and 46214 and find the biggest common factor number .

Step-1: Prime Factorization of 46208

Prime factors of 46208 are 2, 19. Prime factorization of 46208 in exponential form is:

46208 = 2⁷ × 19²

Step-2: Prime Factorization of 46214

Prime factors of 46214 are 2, 7, 3301. Prime factorization of 46214 in exponential form is:

46214 = 2¹ × 7¹ × 3301¹

Step-3: Factors of 46208

List of positive integer factors of 46208 that divides 46208 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 304, 361, 608, 722, 1216, 1444, 2432, 2888, 5776, 11552, 23104

Step-4: Factors of 46214

List of positive integer factors of 46214 that divides 46208 without a remainder.

1, 2, 7, 14, 3301, 6602, 23107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46208 and 46214. The biggest common factor number is the GCF number.
So the greatest common factor 46208 and 46214 is 2.

Also check out the Least Common Multiple of 46208 and 46214