What is the Greatest Common Factor of 21690 and 21700?

Greatest common factor (GCF) of 21690 and 21700 is 10.

GCF(21690,21700) = 10

We will now calculate the prime factors of 21690 and 21700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21690 and 21700.

How to find the GCF of 21690 and 21700?

We will first find the prime factorization of 21690 and 21700. After we will calculate the factors of 21690 and 21700 and find the biggest common factor number .

Step-1: Prime Factorization of 21690

Prime factors of 21690 are 2, 3, 5, 241. Prime factorization of 21690 in exponential form is:

21690 = 2¹ × 3² × 5¹ × 241¹

Step-2: 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-3: Factors of 21690

List of positive integer factors of 21690 that divides 21690 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 241, 482, 723, 1205, 1446, 2169, 2410, 3615, 4338, 7230, 10845

Step-4: Factors of 21700

List of positive integer factors of 21700 that divides 21690 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21690 and 21700. The biggest common factor number is the GCF number.
So the greatest common factor 21690 and 21700 is 10.

Also check out the Least Common Multiple of 21690 and 21700