What is the Greatest Common Factor of 27738 and 27753?

Greatest common factor (GCF) of 27738 and 27753 is 3.

GCF(27738,27753) = 3

We will now calculate the prime factors of 27738 and 27753, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27738 and 27753.

How to find the GCF of 27738 and 27753?

We will first find the prime factorization of 27738 and 27753. After we will calculate the factors of 27738 and 27753 and find the biggest common factor number .

Step-1: Prime Factorization of 27738

Prime factors of 27738 are 2, 3, 23, 67. Prime factorization of 27738 in exponential form is:

27738 = 2¹ × 3² × 23¹ × 67¹

Step-2: Prime Factorization of 27753

Prime factors of 27753 are 3, 11, 29. Prime factorization of 27753 in exponential form is:

27753 = 3¹ × 11¹ × 29²

Step-3: Factors of 27738

List of positive integer factors of 27738 that divides 27738 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 67, 69, 134, 138, 201, 207, 402, 414, 603, 1206, 1541, 3082, 4623, 9246, 13869

Step-4: Factors of 27753

List of positive integer factors of 27753 that divides 27738 without a remainder.

1, 3, 11, 29, 33, 87, 319, 841, 957, 2523, 9251

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27738 and 27753. The biggest common factor number is the GCF number.
So the greatest common factor 27738 and 27753 is 3.

Also check out the Least Common Multiple of 27738 and 27753