What is the Greatest Common Factor of 21700 and 21714?

Greatest common factor (GCF) of 21700 and 21714 is 14.

GCF(21700,21714) = 14

We will now calculate the prime factors of 21700 and 21714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21700 and 21714.

How to find the GCF of 21700 and 21714?

We will first find the prime factorization of 21700 and 21714. After we will calculate the factors of 21700 and 21714 and find the biggest common factor number .

Step-1: Prime Factorization of 21700

Prime factors of 21700 are 2, 5, 7, 31. Prime factorization of 21700 in exponential form is:

21700 = 2² × 5² × 7¹ × 31¹

Step-2: Prime Factorization of 21714

Prime factors of 21714 are 2, 3, 7, 11, 47. Prime factorization of 21714 in exponential form is:

21714 = 2¹ × 3¹ × 7¹ × 11¹ × 47¹

Step-3: Factors of 21700

List of positive integer factors of 21700 that divides 21700 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 31, 35, 50, 62, 70, 100, 124, 140, 155, 175, 217, 310, 350, 434, 620, 700, 775, 868, 1085, 1550, 2170, 3100, 4340, 5425, 10850

Step-4: Factors of 21714

List of positive integer factors of 21714 that divides 21700 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 47, 66, 77, 94, 141, 154, 231, 282, 329, 462, 517, 658, 987, 1034, 1551, 1974, 3102, 3619, 7238, 10857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21700 and 21714. The biggest common factor number is the GCF number.
So the greatest common factor 21700 and 21714 is 14.

Also check out the Least Common Multiple of 21700 and 21714