Factor & Multiple Explorer

What are factors and multiples?

A factor of a number divides it exactly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6, and 12, because each of those divides 12.

A multiple of a number is what you get when you multiply it by a whole number. The multiples of 4 are 4, 8, 12, 16, and so on.

Factors are small and there is a fixed number of them. Multiples go on forever.

What is the greatest common factor?

The greatest common factor of two numbers is the biggest factor they share. Take 24 and 36. Both are divisible by 1, 2, 3, 4, 6, and 12. The biggest of those is 12, so the GCF is 12.

The module lists every factor pair of each number and highlights the ones they share. The biggest highlighted value is the GCF.

What is the least common multiple?

The least common multiple of two numbers is the first multiple they have in common. The multiples of 4 start 4, 8, 12. The multiples of 6 start 6, 12. The first value in both lists is 12, so the LCM is 12.

Factoring a sum

The GCF is useful here. A sum like 36 + 8 can be rewritten with a shared factor pulled out front. The GCF of 36 and 8 is 4, so 36 + 8 = 4 × (9 + 2).

This is the distributive property read backwards. Multiplying 4 by both 9 and 2 gives the two parts back.

What they're learning

• Factors divide a number evenly; multiples are what you get multiplying it.
• Two numbers can share factors and multiples.
• The GCF is the biggest shared factor and the LCM is the first shared multiple.
• A GCF lets you rewrite a sum with the shared factor pulled out front.

Aliases

• Factors and multiples
• GCF and LCM
• Greatest common factor
• Least common multiple
• Factoring

Refresher

A factor divides a number evenly, with nothing left over. A multiple is what you get when you multiply the number by a whole number. The greatest common factor is the biggest factor two numbers share. The least common multiple is the first multiple they share.

Try this together

Two or three minutes at the table is enough.

1. Open Common factors. The numbers are 24 and 36. Ask your kid which factors show up in both lists before you look.
2. Point at the biggest shared factor. That is the GCF, 12.
3. Switch to Common multiples and try 4 and 6. Ask what the first shared multiple will be.
4. Switch to Distributive. The tape splits 24 and 36 into groups of 12. Ask how many groups each number makes.

If two numbers share no factor except 1, the GCF is 1. That is normal, not a mistake.

Words you might hear

• Factor: a number that divides another exactly. 3 is a factor of 12.
• Multiple: a number you get by multiplying by a whole number. 12 is a multiple of 4.
• GCF: the greatest common factor, the biggest factor two numbers share.
• LCM: the least common multiple, the first multiple two numbers share.
• Distributive property: a × (b + c) = a × b + a × c. It lets you factor a sum.

Factors and multiples are easy to mix up. A factor is the same size as the number or smaller. A multiple is the same size or bigger.

Deeper dive

For 24 and 36, the shared factors are 1, 2, 3, 4, 6, and 12, so the GCF is 12. For 4 and 6, the multiples run 4, 8, 12 and 6, 12, so the LCM is 12.

The GCF also lets you rewrite a sum. Since 4 is the GCF of 36 and 8, the sum 36 + 8 becomes 4 × (9 + 2). That is the distributive property run backwards.