Prime factor decomposition

The Maths Habit

Which counters can go in equal rows?Two rows or more.

AYes: 2 rows of 3
BNo: only 1 row
CYes: 3 rows of 3

Is it a prime number?

9No: 3 × 3
2Yes
7Yes
10No: 2 × 5

Prime number
A number with exactly two factors: 1 and itself.
Product
The answer when numbers are multiplied.
Factor tree
A drawing that splits a number into its factors.
Prime factor
A factor that is a prime number.

12 counters go in equal rows. Each way starts a factor tree.

3 rows of 4
123422
2 rows of 6
122623

Both trees end in 2, 2 and 3.  12 = 2 × 2 × 3

12342212 = 2 × 2 × 3
  1. 1Split into a times table fact.Two numbers that multiply to make it. Never 1.
  2. 2Ring the primes. Split the rest.Keep going until every end has a ring.
  3. 3Write the ringed primes with ×.Smallest first.

Write 50 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
5051025
3Write the ringed primes with ×.
50 = 2 × 5 × 5

Write 8 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
82422
3Write the ringed primes with ×.
8 = 2 × 2 × 2

Write 50 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
5051025
3Write the ringed primes with ×.
50 = 2 × 5 × 5
1Split into a times table fact.2Ring the primes. Split the rest.3Write the ringed primes with ×.Primes: 2, 3, 5, 7

Write 63 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
637933
3Write the ringed primes with ×.
63 = 3 × 3 × 7

Write 50 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
5051025
3Write the ringed primes with ×.
50 = 2 × 5 × 5
1Split into a times table fact.2Ring the primes. Split the rest.3Write the ringed primes with ×.Primes: 2, 3, 5, 7

Write 24 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
24462223
3Write the ringed primes with ×.
24 = 2 × 2 × 2 × 3

Write 50 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
5051025
3Write the ringed primes with ×.
50 = 2 × 5 × 5
1Split into a times table fact.2Ring the primes. Split the rest.3Write the ringed primes with ×.Primes: 2, 3, 5, 7

Write 16 as a product of prime factors.

1Split into a times table fact.
2Ring the primes. Split the rest.
16442222
3Write the ringed primes with ×.
16 = 2 × 2 × 2 × 2

1Split into a times table fact.2Ring the primes. Split the rest.3Write the ringed primes with ×.Primes: 2, 3, 5, 7

1Write 81 as a product of prime factors.

81993333
81 = 3 × 3 × 3 × 3

2Write 90 as a product of prime factors.

909103325
90 = 2 × 3 × 3 × 5

3Write 72 as a product of prime factors.

7289243322
72 = 2 × 2 × 2 × 3 × 3

Prime factor decomposition worksheet, page 1

Prime factor decomposition worksheet, page 2

Answer sheet

Is it a product of prime factors?
Thumbs up: right. Thumbs down: wrong.

  1. 20 = 2 × 2 × 5

    Right

  2. 12 = 3 × 4

    Wrong: 4 is not prime

  3. 50 = 2 × 5 × 5

    Right

  4. 30 = 2 × 15

    Wrong: 15 is not prime

  5. 18 = 2 × 3 × 3

    Right

  1. 2 × 2 × 2 is 23. Write 2 × 2 × 2 × 3 with a power.

    23 × 3

  2. What is the smallest number with three different prime factors?

    30 = 2 × 3 × 5

  3. Write 96 as a product of prime factors.

    2 × 2 × 2 × 2 × 2 × 3

  1. Write 70 as a product of prime factors.

    2 × 5 × 7
    707101Split into a timestable fact.2Ring the primes.Split the rest.3Write the ringedprimes with ×.70 =××

  2. Write 27 as a product of prime factors.

    3 × 3 × 3
    271Split into a timestable fact.2Ring the primes.Split the rest.3Write the ringedprimes with ×.27 =××

  3. Write 60 as a product of prime factors.

    2 × 2 × 3 × 5
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