What is the Greatest Common Factor of 90090 and 90100?

Greatest common factor (GCF) of 90090 and 90100 is 10.

GCF(90090,90100) = 10

We will now calculate the prime factors of 90090 and 90100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90090 and 90100.

How to find the GCF of 90090 and 90100?

We will first find the prime factorization of 90090 and 90100. After we will calculate the factors of 90090 and 90100 and find the biggest common factor number .

Step-1: Prime Factorization of 90090

Prime factors of 90090 are 2, 3, 5, 7, 11, 13. Prime factorization of 90090 in exponential form is:

90090 = 2¹ × 3² × 5¹ × 7¹ × 11¹ × 13¹

Step-2: Prime Factorization of 90100

Prime factors of 90100 are 2, 5, 17, 53. Prime factorization of 90100 in exponential form is:

90100 = 2² × 5² × 17¹ × 53¹

Step-3: Factors of 90090

List of positive integer factors of 90090 that divides 90090 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 18, 21, 22, 26, 30, 33, 35, 39, 42, 45, 55, 63, 65, 66, 70, 77, 78, 90, 91, 99, 105, 110, 117, 126, 130, 143, 154, 165, 182, 195, 198, 210, 231, 234, 273, 286, 315, 330, 385, 390, 429, 455, 462, 495, 546, 585, 630, 693, 715, 770, 819, 858, 910, 990, 1001, 1155, 1170, 1287, 1365, 1386, 1430, 1638, 2002, 2145, 2310, 2574, 2730, 3003, 3465, 4095, 4290, 5005, 6006, 6435, 6930, 8190, 9009, 10010, 12870, 15015, 18018, 30030, 45045

Step-4: Factors of 90100

List of positive integer factors of 90100 that divides 90090 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 53, 68, 85, 100, 106, 170, 212, 265, 340, 425, 530, 850, 901, 1060, 1325, 1700, 1802, 2650, 3604, 4505, 5300, 9010, 18020, 22525, 45050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90090 and 90100. The biggest common factor number is the GCF number.
So the greatest common factor 90090 and 90100 is 10.

Also check out the Least Common Multiple of 90090 and 90100