How do you find the greatest common factor (GCF)

The greatest common factor is the largest number that divides every number in the group. Kids can often guess it for 30 and 40, but a guess breaks down on 14, 98 and 35. Prime factors make it mechanical: list the primes of each number, keep only the ones every list shares, and multiply them.

The example at the top shows the whole move on 72 and 24, with the shared 2, 2, 2 and 3 circled, giving 24. The right column raises the bar to the GCF of three numbers, a step past the two-number work of the Grade 6 standard.

That standard is 6.NS.B.4, common factors and multiples. The method also explains why 19, 38 and 95 have a GCF of 19: all three lists contain 19 and nothing else in common.

Begin with 18 and 90 and let your child write both prime lists: 2 x 3 x 3, and 2 x 3 x 3 x 5. Ask, "Which primes can you pair up?" Circling 2, 3 and 3 in both lists gives 18. Many kids expect the answer to be smaller than both numbers. Here it is one of them.

54 and 16 trips kids a different way. They share only one 2, so the GCF is 2, even though both numbers are fairly large. If your child writes 6, ask, "Is there a 3 in the list for 16?"

For 45 and 5, point out that 5 is prime, so the only question is whether 5 divides 45. It does, nine times.

Next time you pack lunch for a group, give your child two numbers: 24 crackers and 36 grapes. "How many identical bags with nothing left over?" The GCF is 12, so 12 bags, each with 2 crackers and 3 grapes.

The same idea lays out a garden bed or a floor with the biggest square tiles that fit both sides exactly.

For a book, The Grapes of Math by Greg Tang turns counting into riddles that reward grouping instead of counting one by one. It builds the same habit: look for the structure first.

Name what your child did: "You checked every list before you multiplied." Next in this series, the least common multiple sheet turns the question around, from the biggest shared factor to the smallest shared multiple.