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Lesson Worksheet: Factors Mathematics

In this worksheet, we will practice finding positive factors of whole numbers using multiplication and division.

Q1:

Which of the following is a valid way to divide 30 players into equal groups, and then share 180 game tokens equally between the groups?

  • A2 groups of 15 players each with 90 tokens per group.
  • B2 groups of 15 players each with 36 tokens per group.
  • C2 groups of 15 players each with 30 tokens per group.
  • D15 groups of 2 players each with 90 tokens per group.
  • E5 groups of 6 players each with 30 tokens per group.

Q2:

Fares is finding factor pairs of 42. Which number is missing from the table?

Factors of 42
142
221
3
67

Q3:

What is the largest factor of 24?

Q4:

Find all the factors of 49.

  • A9 and 40
  • B20 and 29
  • C1, 9, 40, and 49
  • D1, 3, 7, 9, 40, and 49
  • E1, 7, and 49

Q5:

Find the factors of 50.

  • A1,2,5,10,25,50
  • B2,5,10,25
  • C2,5,10,25,50
  • D2,5
  • E1,2,4,5,10,20,25,50

Q6:

How many factors does 93 have?

Q7:

Shady is finding factor pairs of 45. He has drawn a factor rainbow. The factors are written from smallest to greatest and then the factor pairs are joined up.

Which two numbers are missing?

  • A7 and 9
  • B5 and 7
  • C20 and 25
  • D5 and 9
  • E5 and 40

Q8:

Mona is drawing factor rainbows to show all the factor pairs for 20. She writes the factors in order from smallest to largest and draws an arc between each two factors in a pair.

The green arc shows that 2 and 10 are a factor pair, since 2×10=20.

Now it is your turn. Which of the following is a factor rainbow showing all the factor pairs of 24?

  • A
  • B
  • C
  • D
  • E

Q9:

We know that 3×6=18. Pick the true statement.

  • A3 is a multiple of 18.
  • B18 is a factor of 6.
  • C18 is a factor of 3.
  • D6 is a multiple of 18.
  • E3 is a factor of 18.

Q10:

Shady is trying to find all the factors of 72. He could test each of the numbers 1, 2, 3, 4, 5, 6, 7, up to 72, to see if they are factors. But he wants to find a quicker way to find more factors.

He knows that 1 is always a factor, and he sees that 72 is even so 2 must be a factor. He calculates the first two factor pairs and writes them in the table.

He can find factors of 36 to help find factors of 72.

36 is an even number. Complete the equation to find another factor of 72. ×2=36

He notices that 36 is a square number, so it will have a repeated factor. What is the repeated factor?

Continue finding factors to complete the table. Which table shows all the factors of 72?

  • A
    Factors of 72
    1  72
    2  36
    3  24
    4  18
    6  12
    8  9
  • B
    Factors of 72
    1  72
    2  36
    4  9
    6  6
  • C
    Factors of 72
    1  72
    2  36
    3  12
    4  9
    6  6
  • D
    Factors of 72
    172
    236
    963
    1854
    2448
    702
  • E
    Factors of 72
    1  72
    2  36
    4  18
    6  12
    8  9

This lesson includes 48 additional questions and 242 additional question variations for subscribers.

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