What is the Greatest Common Factor of 21735 and 21742?

Greatest common factor (GCF) of 21735 and 21742 is 7.

GCF(21735,21742) = 7

We will now calculate the prime factors of 21735 and 21742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21735 and 21742.

How to find the GCF of 21735 and 21742?

We will first find the prime factorization of 21735 and 21742. After we will calculate the factors of 21735 and 21742 and find the biggest common factor number .

Step-1: Prime Factorization of 21735

Prime factors of 21735 are 3, 5, 7, 23. Prime factorization of 21735 in exponential form is:

21735 = 3³ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 21742

Prime factors of 21742 are 2, 7, 1553. Prime factorization of 21742 in exponential form is:

21742 = 2¹ × 7¹ × 1553¹

Step-3: Factors of 21735

List of positive integer factors of 21735 that divides 21735 without a remainder.

1, 3, 5, 7, 9, 15, 21, 23, 27, 35, 45, 63, 69, 105, 115, 135, 161, 189, 207, 315, 345, 483, 621, 805, 945, 1035, 1449, 2415, 3105, 4347, 7245

Step-4: Factors of 21742

List of positive integer factors of 21742 that divides 21735 without a remainder.

1, 2, 7, 14, 1553, 3106, 10871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21735 and 21742. The biggest common factor number is the GCF number.
So the greatest common factor 21735 and 21742 is 7.

Also check out the Least Common Multiple of 21735 and 21742