30 and 60
30 and 60
30 and 60 have 2, 3, and 5 as factors, as do all other multiples of 30.
Relatively prime is when two numbers have no common factors other than 1. 9 and 4 are two such numbers: 9: 3 x 3 4: 2 x 2
You need at least two numbers to find a GCF. The factors of 6 are 1, 2, 3, 6. In order to have common factors, you have to have two or more numbers to factor. For example, 6 and 14. The factors of 6 are 1, 2, 3, 6 and the factors of 14 are 1, 2, 7, 14. The common factors are 1 and 2, so the GCF is 2.
2 and 3 17
The other factors could be 4 and 5 or 1 and 20.
There are no common factors of 72 because there cannot be common factors without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The prime factors of 72 are 2, 2, 2, 3, and 3.
The squares of all prime numbers above 2 have exactly 3 factors.
30 and 60
The prime factors of 18 are 2, 3 and 3 The prime factors of 30 are 2, 3 and 5 As 2 and 3 are common to both then they are common factors. Further, when numbers share common prime factors, any number which those factors can produce through multiplication is also a common factor of the two original numbers. In this case 2 x 3 = 6, so 2, 3 and 6 are common factors of 18 and 30.
If you multiply two different prime numbers together, you will have a number with four factors, because it will have those two numbers as factors, as well as 1 and itself. Examples: 3 x 5 = 15 which has the factors 1, 3, 5, and 15. 2 x 11 = 22 which has the factors 1, 2, 11, and 22. 5 x 19 = 95 which has the factors 1, 5, 19, and 95.
The prime factors of 144 are 2, 2, 2, 2, 3 and 3 The prime factors of 300 are 2, 2, 3, 5 and 5 So the only prime numbers which are common to both numbers are 2, 2 and 3 = 12