Forty-eight juice boxes and thirty-six granola bars must become identical field-trip bags with nothing left over — the question is simply how many bags. In plain words, list each number's factors and pick the biggest one on both lists. The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48; the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest shared factor is 12, so twelve bags each hold 4 juice boxes and 3 granola bars. Parents packing party favors, teachers grouping students evenly, and cooks portioning ingredients all solve this puzzle. It is the same idea as the GCD, wearing the vocabulary most American classrooms use — and this calculator throws in the least common multiple free.

Type the first number into the Number A box, say 48, and the second into the Number B box, say 36. Read the GCF (a, b) box for the greatest common factor: 12. Check the LCM (a, b) box beside it: 144, the smallest number both divide into evenly. Try 100 and 75 to see a GCF of 25 with an LCM of 300.

With the pre-filled defaults — Number A 48, Number B 36 — the GCF Calculator returns GCF (a, b) 12, LCM (a, b) 144. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.