Factors of 45
45 has 6 factors: 1, 3, 5, 9, 15 and 45. This page shows the pairs that multiply to make 45, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 6 factors of 45
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6 factors
Strictly, every factor also has a negative twin, because two negative numbers multiply to a positive one. School questions almost always mean the positive factors, which is what this page lists.
- Factor pairs
- 1 × 45, 3 × 15 and 5 × 9
- Prime factorization
- 45 = 3² × 5
Why these are the factors of 45
Two numbers form a factor pair of 45 when 45 squares can be arranged into a rectangle with those side lengths and none left over. 45 makes 3 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 45
Split 45 into any two factors, then keep splitting until only primes are left. The bottom row gives 45 = 3 × 3 × 5. Try a different first split: the tree changes shape, but it always ends on the same primes. Click any circled number to split it another way.
45 = 3 × 3 × 5
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 45
Most factors of 45 can be found without dividing. Each rule below looks at one small part of the number, such as the last digit or the digit sum, and each row shows the exact value the rule checks, so you can verify it yourself.
| Rule | It looks at | Verdict |
|---|---|---|
| 2 | The last digit is even. Here it is 5. | No: 45 ÷ 2 leaves remainder 1 |
| 3 | The digits add up to a multiple of 3. Here they add to 9. | Yes: 45 ÷ 3 = 15 |
| 4 | The last two digits form a multiple of 4. Here they are 45. | No: 45 ÷ 4 leaves remainder 1 |
| 5 | The last digit is 0 or 5. Here it is 5. | Yes: 45 ÷ 5 = 9 |
| 6 | It passes both the 2 rule and the 3 rule. | No: 45 ÷ 6 leaves remainder 3 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -6. | No: 45 ÷ 7 leaves remainder 3 |
| 8 | The last three digits form a multiple of 8. Here they are 45. | No: 45 ÷ 8 leaves remainder 5 |
| 9 | The digits add up to a multiple of 9. Here they add to 9. | Yes: 45 ÷ 9 = 5 |
| 10 | The last digit is 0. Here it is 5. | No: 45 ÷ 10 leaves remainder 5 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 1. | No: 45 ÷ 11 leaves remainder 1 |
Multiples of 45
Multiples run in the other direction: they are the numbers 45 divides into exactly. The list starts 45, 90, 135, 180, 225, 270 and goes on forever, growing by 45 each step. Every multiple of 45 has 45 in its own factor list.
The square root of 45
√45 is not a whole number, because 45 sits between the perfect squares 36 and 49. Its exact simplified form is 3√5: the square factor moves out from under the root sign. The decimal 6.708204 is a rounded approximation, not the exact value.
Everything else about 45
| Even or odd | Odd |
|---|---|
| Prime or composite | Composite |
| Number of factors | 6, which matches the rule from 3² × 5: add one to each exponent and multiply. |
| Factors added together | 78 |
| Compared with its own factors | Deficient: the factors below 45 add up to 33, which is less than 45 |
| Numbers below it sharing no factor | 24 of the numbers from 1 to 45 share no factor with 45 |
| 45 squared | 2025 |
| 45 cubed | 91125 |
| A perfect square? | No |
| A perfect cube? | No |
| A triangular number? | Yes |
| Nearest primes | 43 below, 47 above |
| In binary | 101101 |
| In hexadecimal | 2D |
| As a Roman numeral | XLV |
Find the factors of 45 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 45 exactly counts, including 1 and 45 itself.
Frequently asked questions
- What are the factors of 45?
- 45 has 6 factors: 1, 3, 5, 9, 15, 45. Each one divides 45 exactly, with no remainder.
- Is 45 a prime number?
- No, 45 is a composite number. It divides exactly by 3 as well as by 1 and itself, which gives it 6 factors in total.
- What is the prime factorization of 45?
- 45 = 3 × 3 × 5, which is 3² × 5 in exponent form. Whichever pair you split 45 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 45?
- There are 3: 1 × 45, 3 × 15 and 5 × 9. Each pair is a rectangle of 45 squares, with those two numbers as its sides.
- What is the square root of 45?
- √45 is irrational. Its exact simplified form is 3√5; as a decimal it is about 6.708204, which is a rounding rather than the exact value. 45 lies between the perfect squares 36 and 49.
- How many factors does 45 have?
- 6. You can read this off the prime factorization 3² × 5 without listing anything: add one to each exponent and multiply the results.
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