What is the Greatest Common Factor of 21007 and 21014?

Greatest common factor (GCF) of 21007 and 21014 is 7.

GCF(21007,21014) = 7

We will now calculate the prime factors of 21007 and 21014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21007 and 21014.

How to find the GCF of 21007 and 21014?

We will first find the prime factorization of 21007 and 21014. After we will calculate the factors of 21007 and 21014 and find the biggest common factor number .

Step-1: Prime Factorization of 21007

Prime factors of 21007 are 7, 3001. Prime factorization of 21007 in exponential form is:

21007 = 7¹ × 3001¹

Step-2: Prime Factorization of 21014

Prime factors of 21014 are 2, 7, 19, 79. Prime factorization of 21014 in exponential form is:

21014 = 2¹ × 7¹ × 19¹ × 79¹

Step-3: Factors of 21007

List of positive integer factors of 21007 that divides 21007 without a remainder.

1, 7, 3001

Step-4: Factors of 21014

List of positive integer factors of 21014 that divides 21007 without a remainder.

1, 2, 7, 14, 19, 38, 79, 133, 158, 266, 553, 1106, 1501, 3002, 10507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21007 and 21014. The biggest common factor number is the GCF number.
So the greatest common factor 21007 and 21014 is 7.

Also check out the Least Common Multiple of 21007 and 21014