Concept 1 of 6
Factors: Numbers That Divide Evenly
Today's big idea
A factor divides its number exactly, leaving no remainder behind at all.
Factors arrive in pairs, so listing them two at a time stops you missing any.
How it works
👀 What's going on?
Share 20 sweets among friends so that nobody is left short. Only certain group sizes work, and those sizes are the factors of 20.
💡 Here's the trick
Look at the pairs above. A factor divides a number exactly, with no remainder left behind. Factors arrive two at a time, because each one has a partner that multiplies back to the number. 1 is a factor of everything, and the number itself is its own biggest factor.
🪄 How to do it
- 1.Look at the pairs above and start testing from 1.
- 2.When a number divides exactly, write down its partner too.
- 3.Stop once the divisor catches up with its partner.
✍️ Try it
List every factor of 40. Then: how many factors does 49 have?
The pairs for 40 are 1 and 40, 2 and 20, 4 and 10, 5 and 8. In order that is 1, 2, 4, 5, 8, 10, 20, 40. For 49 the pairs are 1 and 49, then 7 and 7, so it has three factors.
⚠️ Watch out
You might be thinking a bigger number always has more factors. It does not. 49 is bigger than 40, yet 49 has only three factors while 40 has eight.
🌟 Why this matters
Splitting a class into equal teams, or a tray of laddoos into equal rows, only works on a factor. Factors also cut a fraction down to its simplest form.
Exam tip: Test divisors in pairs so the big partner at the top never goes missing.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find ALL the factors of 36.”
- 1
Start pairing at 1
1 × 36 ✓ → pair 1 & 36. 🧩
- 2
Try 2, 3, 4
2 × 18 ✓ → 2 & 18. 3 × 12 ✓ → 3 & 12. 4 × 9 ✓ → 4 & 9.
- 3
Try 5 (no)
36 ÷ 5 leaves a remainder. 6 × 6 = 36, so 6 is the middle. STOP.
- 4
List all factors ✓
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap every number that divides 20 with NO remainder.
FACTOR HUNT · ROUND 1 OF 3
20
Found 0 of 6 factors
Quick check
✅ VERIFICATION
Which number is NOT a factor of 60?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Multiples
Multiples of 4: 4, 8, 12, 16, … (forever).