Unknown Factors

Grade 3 · algebra · 81 practice problems · read aloud

🔊 Listen to this explanation

🧩 Finding Unknown Factors

What is an Unknown Factor?

An unknown factor is a missing number in a multiplication problem. Think of it like a puzzle piece that's hiding! We use this skill to solve problems when we know the total and one part, but need to find the other part.

It's useful because it helps us think backwards from the answer to find a missing number, which is a superpower for solving real-world problems!

How to Solve for an Unknown Factor

  1. Look at the equation. Find the blank space or question mark.
  2. Think of the multiplication fact. Ask yourself: "What number, when multiplied by the given factor, equals the total?"
  3. Solve it! Use your multiplication knowledge or related division to find the missing number.
  4. Check your work. Multiply the two factors together. Do they equal the total?

Let's See Some Examples!

Example 1: 4 × ? = 20

Step 1: We know one factor is 4 and the total is 20.

Step 2: Think: "4 times what number equals 20?"

Step 3: 4 × 5 = 20, so the unknown factor is 5!

Step 4: Check: 4 × 5 = 20 ✅

Example 2: ? × 3 = 18

Step 1: We know one factor is 3 and the total is 18.

Step 2: Think: "What number times 3 equals 18?"

Step 3: 6 × 3 = 18, so the unknown factor is 6!

Step 4: Check: 6 × 3 = 18 ✅

⚠️ Common Mistakes to Avoid

  • Adding instead of multiplying: Remember, this is a multiplication problem! For 5 × ? = 15, don't think 5 + 10 = 15.
  • Forgetting to check: Always multiply your answer by the known factor to make sure it gives you the correct total.
  • Getting factors mixed up: The order doesn't matter in multiplication! 3 × 5 is the same as 5 × 3.

💡 Tips & Tricks

  • Think Division: If 6 × ? = 24, you can also think 24 ÷ 6 = ?. Division is the opposite of multiplication!
  • Draw an Array: For 3 × ? = 12, draw 3 rows and see how many dots you need in each row to make 12 total.
  • Use a Fact Family: Remember the three numbers that belong together. For 4, 5, and 20, the facts are: 4×5=20, 5×4=20, 20÷5=4, 20÷4=5.

How to Practice

To get really good at finding unknown factors, try these activities:

  • Create your own "find the missing factor" flashcards.
  • Play online math games that focus on multiplication and division.
  • Ask a friend or family member to give you problems to solve.
  • Look for unknown factors in real life, like figuring out how many packs of markers you need if each pack has 8 markers and you need 24 total.

Practice problems

6 of the 81, worked through step by step — try them before opening the answer.

1 7 × ? = 56

Hint: Think about what number you can multiply by the given number to get the total. For example, if you had 4 × ? = 12, you would need to find what number times 4 equals 12.

Show the answer

Answer: 8

  1. Let the unknown number be x. So the equation becomes: 7 × x = 56
  2. To find x, we need to undo the multiplication by 7. We do this by dividing both sides of the equation by 7.
  3. Divide 56 by 7: 56 ÷ 7 = 8
  4. So x = 8. This means 7 × 8 = 56, which is correct. Final answer: 8

We are solving: 7 × ? = 56

2 8 × ? = 56

Hint: Think about what number you can multiply by the first number to get the result. For example, if you had 4 × ? = 12, you would think about what times 4 equals 12.

Show the answer

Answer: 7

  1. Let the unknown number be x. So the equation is: 8 × x = 56
  2. To find x, we need to undo the multiplication by 8. We do this by dividing both sides of the equation by 8. (8 × x) ÷ 8 = 56 ÷ 8
  3. On the left side, 8 ÷ 8 = 1, so we have: 1 × x = 56 ÷ 8
  4. Calculate 56 ÷ 8: 56 ÷ 8 = 7
  5. So x = 7
  6. Check: 8 × 7 = 56, which matches the original equation. Therefore,

We are solving: 8 × ? = 56 the correct answer is 7.

3 7 × ? = 84

Hint: Think about what number you would multiply by the given factor to get the product. For example, if you had 5 × ? = 20, you would need to find the missing number.

Show the answer

Answer: 12

  1. Let the unknown number be x. So the equation is: 7 × x = 84
  2. To find x, we need to isolate it on one side. Since 7 is multiplied by x, we can undo that by dividing both sides of the equation by 7.
  3. Divide both sides by 7: (7 × x) / 7 = 84 / 7
  4. On the left side, 7/7 = 1, so we have: 1 × x = 84 / 7
  5. Now compute 84 divided by 7: 84 ÷ 7 = 12
  6. Therefore, x = 12 Final answer: 12

We are solving: 7 × ? = 84

4 8 × ? = 72

Hint: Think about what number multiplied by 8 gives the total. For example, if 6 × ? = 42, you would divide 42 by 6 to find the missing number.

Show the answer

Answer: 9

  1. The equation is 8 × ? = 72
  2. To find the missing number, divide 72 by 8
  3. 72 ÷ 8 = 9
  4. Check: 8 × 9 = 72

The answer is 9.

5 ? × 8 = 96

Hint: Think about what number multiplied by 8 gives 96. You can use division to find the missing factor.

Show the answer

Answer: 12

  1. The equation is ? × 8 = 96
  2. To find the missing factor, divide 96 by 8
  3. 96 ÷ 8 = 12
  4. Check: 12 × 8 = 96 ✓ The missing factor is 12.

6 ? × 7 = 84

Hint: Think about what number multiplied by 7 gives 84. You can use division to find the missing factor.

Show the answer

Answer: 12

  1. The equation is ? × 7 = 84
  2. To find the missing factor, divide 84 by 7
  3. 84 ÷ 7 = 12
  4. Check: 12 × 7 = 84 ✓ The missing factor is 12.
Practise this topic — 10 free problems, no signup →