Grade 6 · Math

6th grade Prime factors and perfect squares worksheet

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Prime factors and perfect squares

Grade 6 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Kira wants 54 as a product of primes. You can type 5 × 5 × 7 or 5^2 × 7. What should Kira write?
Milo wants 44 as a product of primes. You can type 5 × 5 × 7 or 5^2 × 7. What should Milo write?
3.
Ren picks a card. Which one shows 88 as a product of primes?
- 2 × 2 × 2 × 11
- 2 × 11
- 8 × 11
- 1 × 2 × 2 × 2 × 11
4.
Tala picks a card. Which one shows 98 as a product of primes?
- 2 × 7
- 1 × 2 × 7 × 7
- 2 × 49
- 2 × 7 × 7
Ari reads 9² in a puzzle. What is 9²?
6.
Esme picks a card. Which number is a perfect square?
- 56
- 51
- 48
- 49
7.
Jun picks a card. Which one is the perfect square?
- 83
- 80
- 90
- 81
8.
Kira picks a card. Which number below is a perfect square?
- 121
- 132
- 123
- 120
Luz's square garden bed has an area of 64 square feet. How long is each side, in feet?
Milo cuts a square from paper. Its area is 100 square centimeters. How long is each side, in centimeters?

6th grade Prime factors and perfect squares worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Prime factors and perfect squares. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell a prime number from a composite number, and I know 1 is neither.
I can split a number into primes with a factor tree and write it as a product of primes.
I can say what 7² means, find a perfect square, and find a square's side from its area.

Standard: state-only (CCSS has no prime-factorization standard; related: 4.OA.B.4 factors, 8.EE.A.2 squares)

Words to know

prime number: A number with exactly two factors: 1 and itself. 2, 3, 5 and 7 are prime.

composite number: A number with more than two factors. 12 has six.

factor tree: A tree that splits a number into factors until every end is a prime.

prime factors: The primes at the ends of the tree. Multiplied, they make the number.

square (n²): A number multiplied by itself. 7² = 7 × 7 = 49.

perfect square: A number you get by multiplying a whole number by itself: 1, 4, 9, 16, 25.

Common mistakes

Your child counted 1 as a prime number.

Your child called an odd number prime. Try testing the number together: can it be split into two smaller numbers other than 1 and itself? For example 9 = 3 × 3.

Your child stopped splitting a factor tree while a number could still be split.

What to say

Ask: how many different factors does a prime have? A prime has exactly two, 1 and itself, and 1 has only one.

Ask: can that number still be split into smaller numbers? Keep going until every end is prime.

Questions parents ask

What is the most common mistake with prime factors and perfect squares?

Your child counted 1 as a prime number.

How can I help my child with prime factors and perfect squares?

Ask: how many different factors does a prime have? A prime has exactly two, 1 and itself, and 1 has only one.

Are these 6th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 6 math

See all grade 6 math

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