Find all factors, factor pairs, and prime factorization of any number instantly. Learn how to factor numbers with step-by-step guide and real-world examples. Free online factor calculator for students and math enthusiasts.
Please provide an integer to calculate its factors and prime factors.
In multiplication, factors are the integers that are multiplied together to find other integers. For example, 6 × 5 = 30. In this example, 6 and 5 are the factors of 30. 1, 2, 3, 10, 15, and 30 would also be factors of 30. Essentially, an integer a is a factor of another integer b, so long as b can be divided by a with no remainder. Factors are important when working with fractions, as well as when trying to find patterns within numbers.
Let's keep this simple. A factor of a number is any whole number that divides evenly into that number. No leftovers. No decimals. Just clean division.
Think of it like this: You have 12 cookies. You want to share them with your friends so everyone gets the same amount. If you have 3 friends, each gets 4 cookies. That works perfectly. So 3 and 4 are factors of 12.
But if you have 5 friends? Each gets 2 cookies, but you have 2 left over. That doesn't work evenly. So 5 is not a factor of 12.
See? Factors are just numbers that play nice with each other.
So you need to find the factors of a number. Maybe it's for homework. Maybe you're just curious. Either way, you've come to the right place.
Our Factor Calculator does all the work for you. Just type in any number, and boom — you get every single factor, listed neatly. No guessing. No missing any.
But here's the thing. A calculator is great, but understanding why those numbers are factors? That's even better. So let's break it down together.
120
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2 60
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2 30
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2 15
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3 5Every number has 1 as a factor. And the number itself is always a factor too. So for the number 24, you already know 1 and 24 are factors. Write them down.
Keep going up. Does 2 divide into 24 evenly? Yes, 24 ÷ 2 = 12. So 2 and 12 are factors. Does 3 work? 24 ÷ 3 = 8. So 3 and 8 are factors. Does 4 work? 24 ÷ 4 = 6. So 4 and 6 are factors.
Here's a cool trick. You don't have to check every single number. Once you get to the square root of your number (or when the numbers start repeating), you're done. For 24, after 4 and 6, the next number is 5. 24 ÷ 5 doesn't work. Then 6 — but you already have 6. So stop.
For 24, the factors are: 1, 2, 3, 4, 6, 8, 12, 24. That's it. You just found all the factors of 24.
You might hear your teacher talk about "factor pairs." Sounds fancy, but it's not.
A factor pair is just two numbers that multiply together to give you the original number. Like 3 and 8 for 24. Or 4 and 6. Or 2 and 12.
Think of them as buddies. They come in pairs. When you find one, you automatically find its partner.
So for 24, the factor pairs are:
Notice how each pair multiplies to 24? That's the whole idea.
Everyone messes up sometimes. Here are the biggest mistakes I see students make.
Mistake 1: Forgetting 1 and the number itself
This is the most common one. People list factors and completely forget that 1 and the number itself count. Don't be that person. Always start with 1 and the number.
Mistake 2: Including numbers that don't divide evenly
If you get a decimal or a remainder, it's not a factor. Only whole numbers count.
Mistake 3: Stopping too early
Some people stop checking after a few numbers. But you need to check all the way up to the square root. Otherwise, you might miss some.
Mistake 4: Confusing factors with multiples
This is a big one. Factors divide into a number. Multiples are what you get when you multiply a number. So 3 is a factor of 12, but 12 is a multiple of 3. Different things.
Once you know factors, you can take it a step further. Prime factorization is when you break a number down into its prime factors. Prime numbers are numbers that only have two factors: 1 and themselves. Like 2, 3, 5, 7, 11, and so on.
Here's how it works for 24:
24 = 2 × 12
12 = 2 × 6
6 = 2 × 3
So the prime factorization of 24 is 2 × 2 × 2 × 3. Or you can write it as 2³ × 3. Our calculator does this too. Just enter your number, and it'll show you the prime factors.
You might be thinking, "When am I ever going to use this?" Fair question. Here are some real-life situations.
You're having a party. You have 36 cupcakes. How many ways can you split them evenly among your guests? Factors tell you. You can have 1, 2, 3, 4, 6, 9, 12, 18, or 36 guests. Each gets the same number.
You want to plant 48 flowers in rows. How many rows can you make? Factors of 48 give you all the options: 1, 2, 3, 4, 6, 8, 12, 16, 24, or 48 rows.
Architects and engineers use factors all the time. If you're tiling a floor that's 60 square feet, you need to know the factors to figure out tile sizes that fit perfectly.
That's it. No sign-ups. No ads. Just pure math magic.
Check your homework. Use the calculator to verify your answers. But try to do it yourself first.
Learn the patterns. Notice how factors of even numbers always include 2. Numbers ending in 0 or 5 always have 5 as a factor.
Use it for big numbers. Finding factors of 1,000 by hand takes forever. The calculator does it in a second.
Compare numbers. Find factors of two different numbers and see what they have in common. That's how you find the greatest common factor.
This confuses so many people. Let me clear it up once and for all.
Numbers that divide into a number. They are smaller than or equal to the number.
Factors of 6: 1, 2, 3, 6
What you get when you multiply a number. They are larger than or equal to the number.
Multiples of 6: 6, 12, 18, 24, 30...
See the difference? Factors go down. Multiples go up.
Here's a trick to remember: Factors are Fewer. Multiples are More.
The number 1 is a factor of every number. It's the universal factor.
Prime numbers only have two factors: 1 and themselves.
Perfect squares (like 4, 9, 16, 25) have an odd number of factors. Try it: factors of 16 are 1, 2, 4, 8, 16. That's 5 factors.
The number 60 has 12 factors. That's why it's used for time (60 seconds, 60 minutes) — it's super divisible.
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A factor is a whole number that divides evenly into another number. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder. Factors are always whole numbers, never decimals or fractions.
Start with 1 and the number itself. Then try dividing by 2, 3, 4, and so on. Stop when you reach the square root of the number. Use our Factor Calculator to check your work instantly.
Factors divide into a number. Multiples are what you get when you multiply a number. For 6, factors are 1, 2, 3, 6. Multiples are 6, 12, 18, 24. Factors are smaller. Multiples are larger.
Yes. 1 divides evenly into every number. So 1 is always a factor. And the number itself is always a factor too. Don't forget these two.
Factor pairs are two numbers that multiply to give the original number. To find them, list all factors and pair them up. For 12, the factor pairs are (1,12), (2,6), and (3,4).
Prime factorization is breaking a number down into prime numbers that multiply together. For 24, it's 2 × 2 × 2 × 3. Our calculator does this automatically.
It's a super common mistake. Just make it a habit. Every time you list factors, write 1 and the number first. Then fill in the rest. You'll never forget again.
Yes. Perfect squares like 4, 9, 16, and 25 have an odd number of factors. For example, factors of 16 are 1, 2, 4, 8, 16. That's 5 factors. Most other numbers have an even number.
Do the problem yourself first. Then use the calculator to check your answer. If you got it wrong, look at the calculator's result and figure out where you messed up. That's how you learn.
Factors help with splitting things evenly, organizing items into groups, building and construction, and even cooking. Any time you need to divide something into equal parts, factors come in handy.
Find all factors of both numbers. Then look for the largest number that appears in both lists. For example, factors of 12 are 1,2,3,4,6,12. Factors of 18 are 1,2,3,6,9,18. The GCF is 6.
Use our Factor Calculator. It's the fastest way. But if you're doing it by hand, make sure you checked every number up to the square root. If you did, you're good.