Factors divide the number evenly. Multiples are what you get by multiplying it. The GCF is the largest shared factor. The LCM is the smallest shared multiple. Primes, consecutives, and remainders are in integers on ACT Math.
Factor or multiple
3 is a factor of 12 because 12 ÷ 3 is a whole number. 24 is a multiple of 12 because 12 × 2 = 24. “Divisible by” means factor. “A multiple of” means you can land on it by counting in steps of that size.
The GCF of 12 and 18 is 6. The LCM is 36. If the numbers are small, list the factors or the first few multiples and circle the overlap. Odd and even shortcuts that help that list are in odd, even, positive, and negative.
Where it shows up
Shared timing — two cycles that start together — is an LCM. Splitting into the largest equal groups is a GCF. The formula list these sit near is in ACT Math formulas. Probability, which sometimes starts from a count of factors, is in probability problems.
The bottom line
Factors go into the number. Multiples are the number stretched out. GCF is the biggest shared divisor. LCM is the smallest shared multiple.
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