What is the Greatest Common Factor of 54735 and 54740?

Greatest common factor (GCF) of 54735 and 54740 is 5.

GCF(54735,54740) = 5

We will now calculate the prime factors of 54735 and 54740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54735 and 54740.

How to find the GCF of 54735 and 54740?

We will first find the prime factorization of 54735 and 54740. After we will calculate the factors of 54735 and 54740 and find the biggest common factor number .

Step-1: Prime Factorization of 54735

Prime factors of 54735 are 3, 5, 41, 89. Prime factorization of 54735 in exponential form is:

54735 = 3¹ × 5¹ × 41¹ × 89¹

Step-2: Prime Factorization of 54740

Prime factors of 54740 are 2, 5, 7, 17, 23. Prime factorization of 54740 in exponential form is:

54740 = 2² × 5¹ × 7¹ × 17¹ × 23¹

Step-3: Factors of 54735

List of positive integer factors of 54735 that divides 54735 without a remainder.

1, 3, 5, 15, 41, 89, 123, 205, 267, 445, 615, 1335, 3649, 10947, 18245

Step-4: Factors of 54740

List of positive integer factors of 54740 that divides 54735 without a remainder.

1, 2, 4, 5, 7, 10, 14, 17, 20, 23, 28, 34, 35, 46, 68, 70, 85, 92, 115, 119, 140, 161, 170, 230, 238, 322, 340, 391, 460, 476, 595, 644, 782, 805, 1190, 1564, 1610, 1955, 2380, 2737, 3220, 3910, 5474, 7820, 10948, 13685, 27370

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54735 and 54740. The biggest common factor number is the GCF number.
So the greatest common factor 54735 and 54740 is 5.

Also check out the Least Common Multiple of 54735 and 54740