8 Times What Is 24? | Reverse Multiplication Made Easy

Eight equal groups make twenty-four when each group has three, so 8 × 3 = 24.

You’re staring at a question that looks backwards: “8 times what is 24?” It’s a multiplication fact, just written from the other side. Instead of being told both factors, you’re told the product (24) and one factor (8), then asked to find the missing factor.

Once you know the trick, it stops feeling tricky. You’ll use one simple idea: multiplication and division undo each other. Then you’ll learn a couple of fast checks so you can spot mistakes before you turn in the work.

What “8 times what is 24” is asking

Read it like this: eight multiplied by some number equals twenty-four. In math symbols, that’s:

8 × ? = 24

The question mark is the missing factor. Your job is to find the number that makes the statement true.

8 Times What Is 24? And why the answer is 3

If 8 × ? = 24, then the missing number must be 3, because 8 × 3 = 24.

You can get that answer in more than one way. The cleanest route is division: 24 ÷ 8 = 3. If you’re allowed to use division, you’re done in one step.

If you’re building the idea from scratch, you can also think in groups: split 24 items into 8 equal groups. If each group ends up with 3 items, the groups stay equal and all 24 items get used.

Solving 8 times equals 24 using division

Division is the “reverse” of multiplication. When you see “8 times what is 24,” you can flip it into a division question: “24 divided by 8 equals what?”

Step-by-step method

1. Write the equation: 8 × ? = 24.
2. Divide the product by the known factor: 24 ÷ 8.
3. Compute the division: 24 ÷ 8 = 3.
4. Check by multiplying: 8 × 3 = 24.

That last check matters because it catches slips like dividing by the wrong number or copying 24 as 42. A five-second check can save a full point.

Two mental math routes when you can’t grab a calculator

On homework, quizzes, or oral practice, you might want a no-scratch-paper way to get the missing factor. Here are two that stay quick.

Route 1: Use known facts and scale

If you know 8 × 2 = 16, you can see how far 16 is from 24. The gap is 8. One more group of 8 takes you from 16 to 24, so the factor goes from 2 to 3.

Route 2: Count by eights

Say the multiples of 8 in order: 8, 16, 24. Count how many steps it took to reach 24. You landed on the third multiple, so 8 × 3 = 24.

This method works well when the product is a clean multiple that shows up early in the counting pattern.

Visual models that make the missing factor obvious

Sometimes the best way to learn a fact is to see it. Visual models turn “8 times what is 24” into something you can point at.

Equal groups

Draw 8 circles. Put dots into each circle until you reach 24 dots total, keeping the circles balanced. When each circle has 3 dots, you hit 24 with no leftovers. That tells you the missing factor is 3.

Array model

Make a rectangle with 8 rows. Fill in 24 total squares. When you place 3 squares in each row, the array is complete: 8 rows × 3 squares per row = 24 squares.

Number line hops

Start at 0 on a number line. Hop forward by 8 each time. After 3 hops you land on 24. The hop count is the missing factor.

Common mistakes and fast fixes

Most wrong answers come from the same small set of mix-ups. If you know them, you’ll dodge them.

Mixing up the direction

Some learners do 8 ÷ 24 instead of 24 ÷ 8. A quick cue: the bigger number goes inside the division when you’re finding a missing factor from a product. Here, 24 is the product, so start with 24.

Guessing a factor without checking

Guessing can work if you check right away. If someone guesses 4, the check 8 × 4 = 32 shows it doesn’t match 24, so the guess gets tossed.

Dropping the meaning of “times”

“Times” means multiply, not add. If you add 8 + 24, you get 32, and that doesn’t fit the original statement. Keep it tied to multiplication: factor × factor = product.

Quick reference table for “8 × ? = 24” and similar problems

When you practice missing-factor questions, you’ll see the same structures again and again. The table below shows several ways to spot the missing factor, plus the check that proves it.

Problem form	Fast method	Check that confirms
8 × ? = 24	24 ÷ 8 = 3	8 × 3 = 24
? × 8 = 24	24 ÷ 8 = 3	3 × 8 = 24
24 ÷ 8 = ?	Divide: 24 ÷ 8	? × 8 = 24
8 × ? = 16	Count by 8s: 8, 16	8 × 2 = 16
8 × ? = 32	Half of 32 is 16, then double: 4	8 × 4 = 32
8 × ? = 40	8 × 5 = 40 (known fact)	40 ÷ 8 = 5
8 × ? = 56	7 groups of 8 make 56	56 ÷ 8 = 7
8 × ? = 72	9 groups of 8 make 72	72 ÷ 8 = 9

Why inverse operations work every time

Multiplication and division are paired operations. If you multiply a number by 8, you can undo that action by dividing by 8. That’s why the missing-factor move is so reliable.

Think of it like tying and untying a knot. Multiply to tie the numbers together into a product. Divide to untie and recover a factor.

When the division doesn’t land on a whole number

Some worksheets swap 24 for a number that isn’t a clean multiple of 8. If you try 25 ÷ 8, you won’t get a whole number. That’s a signal that no whole-number factor makes 8 × ? equal 25.

That doesn’t mean the question is broken. It just changes the type of answer. In fraction form, 25 ÷ 8 equals 25/8, and in decimal form it equals 3.125. You can still check it: 8 × (25/8) returns 25. In early grades, teachers often pick products like 24 that stay in whole numbers so the focus stays on the inverse idea.

If you want to see this written as a rule, the basic idea shows up in the grade-school operations standards for multiplication and division. The wording may vary by curriculum, but the relationship stays the same. The Common Core 3.OA.A.1 standard lays out multiplication as equal groups and arrays, which matches the models you used above.

Build the fact so it sticks in your head

Memorizing facts can feel like grinding. A small pattern can make this one stick without a lot of repetition.

Link it to easier facts

Start with 8 × 1 = 8. Add one more 8 to get 8 × 2 = 16. Add one more 8 to get 8 × 3 = 24. That’s three steps, each one clear.

Use factor pairs of 24

Twenty-four can be made from these factor pairs: 1 × 24, 2 × 12, 3 × 8, 4 × 6. When you see an 8 in the question, your eyes can jump straight to the pair 3 × 8.

Say it out loud

Try this: “Eight threes are twenty-four.” It’s short, it has rhythm, and it lands as one chunk.

Practice set with instant checks

Try these in order. After each one, use the check step right away. If the check doesn’t match, redo the division.

1. 8 × ? = 48
2. 8 × ? = 64
3. 8 × ? = 80
4. 8 × ? = 96
5. ? × 8 = 40
6. 72 ÷ 8 = ?

When you solve them, you’re training the same move you used for 24: product ÷ known factor = missing factor. Then multiply back to confirm.

Related facts table for the 8s family around 24

This table puts the “8s” facts near 24 in one spot. It can help when you’re studying, checking homework, or making flash cards.

Factor pair	Multiplication fact	Division check
8 and 1	8 × 1 = 8	8 ÷ 8 = 1
8 and 2	8 × 2 = 16	16 ÷ 8 = 2
8 and 3	8 × 3 = 24	24 ÷ 8 = 3
8 and 4	8 × 4 = 32	32 ÷ 8 = 4
8 and 5	8 × 5 = 40	40 ÷ 8 = 5
8 and 6	8 × 6 = 48	48 ÷ 8 = 6
8 and 7	8 × 7 = 56	56 ÷ 8 = 7
8 and 8	8 × 8 = 64	64 ÷ 8 = 8
8 and 9	8 × 9 = 72	72 ÷ 8 = 9
8 and 10	8 × 10 = 80	80 ÷ 8 = 10
8 and 12	8 × 12 = 96	96 ÷ 8 = 12

Answer check: what to write on the page

If your worksheet expects a single number, write 3.

If it expects a full sentence, you can write: “8 times 3 is 24.”

If it expects a shown step, write: “24 ÷ 8 = 3,” then “8 × 3 = 24.”

That’s all the problem needs: one clean move and one clean check. After a few rounds of practice, this style of question starts feeling like a free point.

If you want extra practice with arrays and equal groups, the Khan Academy introduction to multiplication page has short lessons that match the models used here.