What is the Greatest Common Factor of 30240 and 30260?

Greatest common factor (GCF) of 30240 and 30260 is 20.

GCF(30240,30260) = 20

We will now calculate the prime factors of 30240 and 30260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30240 and 30260.

How to find the GCF of 30240 and 30260?

We will first find the prime factorization of 30240 and 30260. After we will calculate the factors of 30240 and 30260 and find the biggest common factor number .

Step-1: Prime Factorization of 30240

Prime factors of 30240 are 2, 3, 5, 7. Prime factorization of 30240 in exponential form is:

30240 = 2⁵ × 3³ × 5¹ × 7¹

Step-2: Prime Factorization of 30260

Prime factors of 30260 are 2, 5, 17, 89. Prime factorization of 30260 in exponential form is:

30260 = 2² × 5¹ × 17¹ × 89¹

Step-3: Factors of 30240

List of positive integer factors of 30240 that divides 30240 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 336, 360, 378, 420, 432, 480, 504, 540, 560, 630, 672, 720, 756, 840, 864, 945, 1008, 1080, 1120, 1260, 1440, 1512, 1680, 1890, 2016, 2160, 2520, 3024, 3360, 3780, 4320, 5040, 6048, 7560, 10080, 15120

Step-4: Factors of 30260

List of positive integer factors of 30260 that divides 30240 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 89, 170, 178, 340, 356, 445, 890, 1513, 1780, 3026, 6052, 7565, 15130

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30240 and 30260. The biggest common factor number is the GCF number.
So the greatest common factor 30240 and 30260 is 20.

Also check out the Least Common Multiple of 30240 and 30260