What is the Greatest Common Factor of 35214 and 35228?

Greatest common factor (GCF) of 35214 and 35228 is 2.

GCF(35214,35228) = 2

We will now calculate the prime factors of 35214 and 35228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35214 and 35228.

How to find the GCF of 35214 and 35228?

We will first find the prime factorization of 35214 and 35228. After we will calculate the factors of 35214 and 35228 and find the biggest common factor number .

Step-1: Prime Factorization of 35214

Prime factors of 35214 are 2, 3, 5869. Prime factorization of 35214 in exponential form is:

35214 = 2¹ × 3¹ × 5869¹

Step-2: Prime Factorization of 35228

Prime factors of 35228 are 2, 8807. Prime factorization of 35228 in exponential form is:

35228 = 2² × 8807¹

Step-3: Factors of 35214

List of positive integer factors of 35214 that divides 35214 without a remainder.

1, 2, 3, 6, 5869, 11738, 17607

Step-4: Factors of 35228

List of positive integer factors of 35228 that divides 35214 without a remainder.

1, 2, 4, 8807, 17614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35214 and 35228. The biggest common factor number is the GCF number.
So the greatest common factor 35214 and 35228 is 2.

Also check out the Least Common Multiple of 35214 and 35228