Factors - 1, 2, 3, 15, 30
Multiples 0, 30, 60, 90, 120, 150...
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5, 10, 15 and 30.
Factors: 1, 3, 5, 15 Multiples: 15, 30, 45, 60, 75 and so on.
Factors are numbers which divide another number by a whole number amount. 1 X 30 but this can be excluded since 1 and the number itself are always factors of a non-zero integer. 2 X 15 3 X 10 5 X 6 so the factors of 30 are 2,3,5,6,10, and 15 Multiples are other numbers that a given number will factor into. Some multiples of thirty are 30,60,90,120,150,180, and 210. There are, however, infinite multiples of thirty.
To find common multiples of two numbers, you first have to break them down into their prime factors. In this case, the prime factors of 30 and 75 are: 30 = 2x3x5 75 = 3x5x5 The next step is to identify and discard any duplicate common factors. In this case both numbers have a 3 and a 5 as prime factors, so we can discard one of each. Taking all the other prime factors (2, 3, 5 and 5) and multiplying them together will give us the LCM: 2x3x5x5 = 150. Thus the lowest common multiple of 30 and 75 is 150. To find other common multiples, you just multiply this LCM by any integer. For instance, 150x2, 150x3, 150x4 and so on. This means the first few common multiples of 30 and 75 are 150, 300, 450 and 600.
Factors of the number will also be factors of the number's multiples. Multiples of the number will also be multiples of the number's factors.