Worksheet: Prime Factorization

In this worksheet, we will practice using different strategies, such as repeated division and the factor tree, to find prime factorization.

Q1:

Factorise the given numbers into the prime factors by completing the figure below.

  • A 5 × 1 7 × 1 1
  • B 5 × 1 7 × 5 5
  • C 8 5 × 1 7 × 1 1
  • D 5 × 1 8 7 × 1 1

Q2:

Complete the factor tree.

  • A14, 11, 3
  • B14, 7, 3
  • C33, 7, 11
  • D33, 11, 3

Q3:

Find the prime factors of 490.

  • A4, 9, 11
  • B7, 10, 49
  • C2, 5, 7
  • D2, 7, 9

Q4:

There are 72 people in a graduation ceremony. List all the factors of 72, and state what type of number it is.

  • A 2 , 3 , 4 , 6 , 8 , 9 , 1 2 , 1 8 , 2 4 , 3 6 , 7 2 , prime
  • B 1 , 2 , 3 , 4 , 6 , 8 , 9 , 1 2 , 1 8 , 2 4 , 3 6 , 7 2 , composite
  • C 1 , 2 , 3 , 4 , 6 , 8 , 9 , 1 2 , 1 8 , 2 4 , 3 6 , 7 2 , prime
  • D 2 , 3 , 4 , 6 , 8 , 9 , 1 2 , 1 8 , 2 4 , 3 6 , 7 2 , composite
  • E 2 , 3 , 4 , 6 , 8 , 9 , 1 2 , 1 8 , 2 4 , 3 6 , composite

Q5:

Write 46 as a product of primes.

  • A 3 × 2 3
  • B 2 × 3 × 2 3
  • C 2 × 2 3
  • D 1 × 4 6
  • E 2 × 2 × 2 3

Q6:

A book consists of 483 pages. Write this number as a product of prime numbers.

  • A 7 2 3
  • B 3 2 3
  • C 7 7 2 3
  • D 3 3 2 3
  • E 7 3 2 3

Q7:

Which of the numbers 22, 67, 21, 36, 48, and 8 has a prime factorization of exactly two factors?

  • A48, 8
  • B22
  • C22, 21
  • D21
  • E67, 36

Q8:

Which of the following is the prime factorization of 10?

  • A10
  • B2
  • C 1 0 × 1
  • D5
  • E 2 × 5

Q9:

Which of the following is the prime factorization of 49?

  • A7
  • B49
  • C1
  • D 4 9 × 1
  • E 7 × 7

Q10:

I am an odd number between 40 and 54. I have exactly one prime factor that is not me. What number am I?

  • A48
  • B52
  • C51
  • D49
  • E47

Q11:

Find the smallest number whose prime factors are 3, 5, and 7.

  • A102
  • B110
  • C15
  • D105

Q12:

Which of the following is the prime factorization of 18?

  • A18
  • B2
  • C3
  • D 2 × 3 × 3
  • E 2 × 9

Q13:

Find the number whose prime factors are 5 and 7.

  • A25
  • B168
  • C175
  • D49

Q14:

Find the missing number in the given Venn diagram.

Q15:

Find the prime number where the sum of the factors is 84.

Q16:

Find the prime number where the difference of the factors is 40.

Q17:

Find the two numbers where 11, 3, 5, and 11 are the prime factors of the first number and 2, 17, 17, and 5 are the prime factors of the second number.

  • AThe first number is 165 and the second number is 578.
  • BThe first number is 1,826 and the second number is 2,895.
  • CThe first number is 224 and the second number is 418.
  • DThe first number is 1,815 and the second number is 2,890.

Q18:

Venn diagrams can describe prime factors. Find the missing number in this Venn Diagram.

Q19:

Find the missing numbers in the given Venn diagram before answering the following questions.

Find the greatest common factor of 35 and 55.

Find the least common multiple of 35 and 55.

Q20:

Venn diagrams are useful for finding the greatest common factor and the least common multiple of two numbers.

Write 30 as a product of its prime factors.

  • A 3 × 5 × 5
  • B 2 × 3 × 5
  • C 3 × 1 0
  • D 5 × 6
  • E 3 × 3 × 5

Write 75 as a product of its prime factors.

  • A 5 × 5 × 5
  • B 3 × 5 × 5
  • C 3 × 3 × 5
  • D 5 × 1 5
  • E 3 × 2 5

Which of the following diagrams displays a correct Venn diagram?

  • A(B)
  • B(C)
  • C(A)
  • D(D)

Q21:

Venn diagrams are used to find the greatest common factor and the least common multiple of two numbers.

Write 18 as a product of its prime factors.

  • A 6 × 3
  • B 2 × 3 × 3
  • C 3 × 2 × 2
  • D 3 × 3 × 3
  • E 2 × 9

Write 60 as a product of its prime factors.

  • A 2 × 3 × 3 × 5
  • B 2 × 3 × 5
  • C 5 × 1 2
  • D 6 × 1 0
  • E 2 × 2 × 3 × 5

Which of the following diagrams displays a correct Venn diagram?

  • A(B)
  • B(A)
  • C(C)
  • D(D)

Q22:

Round the number 38.1 to the nearest whole number, and then express it as a product of primes.

  • A 3 8 , 2 1 7
  • B 3 8 , 1 9 1 7
  • C 3 7 , 1 9 2
  • D 3 7 , 2 1 7
  • E 3 8 , 1 9 2

Q23:

If Michael’s height is 2 feet and 5 inches, express, in inches, his height as a product of primes.

  • A 5 2 4
  • B 1 2 9
  • C 2 5
  • D 1 1 9
  • E 1 2 4

Q24:

Express 9 as a product of primes.

  • A 3 × 3 × 3
  • B 4 × 4
  • C 2 × 2 × 2
  • D 2 × 2 × 2 × 2
  • E 3 × 3

Q25:

What is the largest prime factor of 120?

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