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Find Factor Pairs for Whole Numbers up to 100

Students systematically find all factor pairs for any whole number from 1 to 100 by testing divisibility starting from 1 and working up to the square root of the number. They record pairs and recognize that some numbers have many factor pairs while others have only one.

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Find Factor Pairs for Whole Numbers up to 100

Grade 4 · Factors, Multiples, Primes, and Composites · question 1 of 3

0 of 20

20 rungs. A star at the top.

20 = 4 ×

How it is taught

0:00 of 4:17

A factor pair is two whole numbers that multiply to the target.

Start at 1 and keep going until the pairs meet.

Read it: Test the numbers in order

Which pairs of numbers multiply to make 24? Test 1, 2, 3 and on: 1 × 24, 2 × 12, 3 × 8, 4 × 6. At 6 the pair is one already found.

  1. Start at 1 and test each number in order.
  2. If it divides with no remainder, write the pair it makes.
  3. Stop when the next pair would be one you have already found.

Every factor pair has one number that is the smaller of the two, so testing in order finds each pair once.

A number with only the pair 1 and itself is prime; any other pair makes it composite.

1 has only one factor, so it is neither prime nor composite.

Each number that divides with no remainder makes a factor pair.

Calling 9 prime because it is odd.

9 = 3 × 3 is another factor pair, so 9 is composite. Odd numbers can be composite too.

How many factor pairs does 36 have? — 5. 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6: 5 pairs.

Factor pairs of 24

A factor pair is two whole numbers that multiply to make a target number. Today, let's find every factor pair of twenty-four.

We'll test each whole number, starting from one, and write down the pairs we find.

Does one work? Yes — one times twenty-four equals twenty-four.

So our first factor pair is one and twenty-four.

Does two work? Yes — two times twelve equals twenty-four.

Add two and twelve to our list.

Does three work? Yes — three times eight equals twenty-four.

Three and eight goes on the list too.

Does four work? Yes — four times six equals twenty-four.

Four and six — another pair found!

Now try five. Five times five is twenty-five — already past twenty-four. We can stop, because anything bigger would just repeat a pair we already have.

What pairs multiply to make 24?Factor pairs of 24TARGET24Factor pairs:1 × 242 × 123 × 84 × 6Try 1: 1 × 24 = 24 ✓Try 2: 2 × 12 = 24 ✓Try 3: 3 × 8 = 24 ✓Try 4: 4 × 6 = 24 ✓Try 5: 5 × 5 = 25 — too big!Stop — we've found every pair.Stop testing once N × N passes the target.TOTAL4factor pairs
Grade 4 · Find every pair that multiplies to 24

Twenty-four has four factor pairs. Awesome work — you're thinking like a mathematician!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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