What is the Greatest Common Factor of 61740 and 61754?

Greatest common factor (GCF) of 61740 and 61754 is 14.

GCF(61740,61754) = 14

We will now calculate the prime factors of 61740 and 61754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61740 and 61754.

How to find the GCF of 61740 and 61754?

We will first find the prime factorization of 61740 and 61754. After we will calculate the factors of 61740 and 61754 and find the biggest common factor number .

Step-1: Prime Factorization of 61740

Prime factors of 61740 are 2, 3, 5, 7. Prime factorization of 61740 in exponential form is:

61740 = 2² × 3² × 5¹ × 7³

Step-2: Prime Factorization of 61754

Prime factors of 61754 are 2, 7, 11, 401. Prime factorization of 61754 in exponential form is:

61754 = 2¹ × 7¹ × 11¹ × 401¹

Step-3: Factors of 61740

List of positive integer factors of 61740 that divides 61740 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 49, 60, 63, 70, 84, 90, 98, 105, 126, 140, 147, 180, 196, 210, 245, 252, 294, 315, 343, 420, 441, 490, 588, 630, 686, 735, 882, 980, 1029, 1260, 1372, 1470, 1715, 1764, 2058, 2205, 2940, 3087, 3430, 4116, 4410, 5145, 6174, 6860, 8820, 10290, 12348, 15435, 20580, 30870

Step-4: Factors of 61754

List of positive integer factors of 61754 that divides 61740 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 401, 802, 2807, 4411, 5614, 8822, 30877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61740 and 61754. The biggest common factor number is the GCF number.
So the greatest common factor 61740 and 61754 is 14.

Also check out the Least Common Multiple of 61740 and 61754