What is the Greatest Common Factor of 21754 and 21770?

Greatest common factor (GCF) of 21754 and 21770 is 2.

GCF(21754,21770) = 2

We will now calculate the prime factors of 21754 and 21770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21754 and 21770.

How to find the GCF of 21754 and 21770?

We will first find the prime factorization of 21754 and 21770. After we will calculate the factors of 21754 and 21770 and find the biggest common factor number .

Step-1: Prime Factorization of 21754

Prime factors of 21754 are 2, 73, 149. Prime factorization of 21754 in exponential form is:

21754 = 2¹ × 73¹ × 149¹

Step-2: Prime Factorization of 21770

Prime factors of 21770 are 2, 5, 7, 311. Prime factorization of 21770 in exponential form is:

21770 = 2¹ × 5¹ × 7¹ × 311¹

Step-3: Factors of 21754

List of positive integer factors of 21754 that divides 21754 without a remainder.

1, 2, 73, 146, 149, 298, 10877

Step-4: Factors of 21770

List of positive integer factors of 21770 that divides 21754 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 311, 622, 1555, 2177, 3110, 4354, 10885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21754 and 21770. The biggest common factor number is the GCF number.
So the greatest common factor 21754 and 21770 is 2.

Also check out the Least Common Multiple of 21754 and 21770