What is the Greatest Common Factor of 21735 and 21749?

Greatest common factor (GCF) of 21735 and 21749 is 7.

GCF(21735,21749) = 7

We will now calculate the prime factors of 21735 and 21749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21735 and 21749.

How to find the GCF of 21735 and 21749?

We will first find the prime factorization of 21735 and 21749. After we will calculate the factors of 21735 and 21749 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 21749

Prime factors of 21749 are 7, 13, 239. Prime factorization of 21749 in exponential form is:

21749 = 7¹ × 13¹ × 239¹

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 21749

List of positive integer factors of 21749 that divides 21735 without a remainder.

1, 7, 13, 91, 239, 1673, 3107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21735 and 21749. The biggest common factor number is the GCF number.
So the greatest common factor 21735 and 21749 is 7.

Also check out the Least Common Multiple of 21735 and 21749