What is the Greatest Common Factor of 61740 and 61758?

Greatest common factor (GCF) of 61740 and 61758 is 18.

GCF(61740,61758) = 18

We will now calculate the prime factors of 61740 and 61758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61740 and 61758.

How to find the GCF of 61740 and 61758?

We will first find the prime factorization of 61740 and 61758. After we will calculate the factors of 61740 and 61758 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 61758

Prime factors of 61758 are 2, 3, 47, 73. Prime factorization of 61758 in exponential form is:

61758 = 2¹ × 3² × 47¹ × 73¹

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 61758

List of positive integer factors of 61758 that divides 61740 without a remainder.

1, 2, 3, 6, 9, 18, 47, 73, 94, 141, 146, 219, 282, 423, 438, 657, 846, 1314, 3431, 6862, 10293, 20586, 30879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61740 and 61758. The biggest common factor number is the GCF number.
So the greatest common factor 61740 and 61758 is 18.

Also check out the Least Common Multiple of 61740 and 61758