What is the Greatest Common Factor of 71204 and 71214?

Greatest common factor (GCF) of 71204 and 71214 is 2.

GCF(71204,71214) = 2

We will now calculate the prime factors of 71204 and 71214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71204 and 71214.

How to find the GCF of 71204 and 71214?

We will first find the prime factorization of 71204 and 71214. After we will calculate the factors of 71204 and 71214 and find the biggest common factor number .

Step-1: Prime Factorization of 71204

Prime factors of 71204 are 2, 7, 2543. Prime factorization of 71204 in exponential form is:

71204 = 2² × 7¹ × 2543¹

Step-2: Prime Factorization of 71214

Prime factors of 71214 are 2, 3, 11, 13, 83. Prime factorization of 71214 in exponential form is:

71214 = 2¹ × 3¹ × 11¹ × 13¹ × 83¹

Step-3: Factors of 71204

List of positive integer factors of 71204 that divides 71204 without a remainder.

1, 2, 4, 7, 14, 28, 2543, 5086, 10172, 17801, 35602

Step-4: Factors of 71214

List of positive integer factors of 71214 that divides 71204 without a remainder.

1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 83, 143, 166, 249, 286, 429, 498, 858, 913, 1079, 1826, 2158, 2739, 3237, 5478, 6474, 11869, 23738, 35607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71204 and 71214. The biggest common factor number is the GCF number.
So the greatest common factor 71204 and 71214 is 2.

Also check out the Least Common Multiple of 71204 and 71214