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# Factors of 45 | Factor Pairs of 45

Factors of 45 are those numbers that, when multiplied together, give the result 45. We can also say that a factor is a number that divides a number completely, leaving zero as a remainder. To find the factors of 45, we will use the division method here.

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## Factors of 45

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### How to Find factors of 45?

To calculate the factors of any number, here 156 in this case, we have to find all the numbers which will divide 156 without leaving any remainder. We start with the number 1, then go on checking the numbers 2, 3, 4, 5, 6, 7, etc. The number 1 and the number itself are always factors of the given number.

(i) 45 ÷ 1 = 45

Gives the remainder 0 and so is divisible by 45. So please put it on your factor list.

(ii) 45 ÷ 2 = 22.5

Gives a remainder of 22.5, not being thoroughly divided. So we will not write two on the list.

(iii) 45 ÷ 3 = 15

Gives the remainder 0 and so is divisible by 15. So please put it on your factor list.

(iv) 45 ÷ 4 = 11.25

Gives the remainder 11.25, not being thoroughly divided. So we will not write five on the list.

(v) 45 ÷ 5 = 9

Gives the remainder 0 and so is divisible by 9. So please put it on your factor list.

(vi) 45 ÷ 6 = 7.5

Gives a remainder of 7.5, not being thoroughly divided. So we will not write seven on the list.

(vii) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 3, 5, 9, 15, 45 are a factor of 45.

### Factors of – 45

As – 3 and – 15 are negative factors, because you get a positive number by multiplying two negatives, like (- 3) × (- 15) = 45.

So, – 1, – 3, – 5, – 9, – 15 and – 45 are negative factor of 45.

### All factors of 45

Here is a list of all the positive and negative factors of 45 in numerical order.

Positive Factors of 45 = 1, 3, 5, 9,15, 45
Negative Factors of 45 = – 1, – 3, – 5, – 9, – 15, – 45

So, – 1, – 3, – 5, – 9, – 15, – 45, 1, 3, 5, 9,15, 45 All factors of 45.

### Factor pairs of 45

1 and 45 are a factor pair of 45 since 1 x 45 = 45
3 and 15 are a factor pair of 45 since 3 x 15 = 45
5 and 9 are a factor pair of 45 since 5 x 9 = 45

So, (1, 45), (3, 15), (5, 9) are factors of 45 in pairs.

### Negative pair factors of 45

(-1) × (- 45) = (-1, – 45)
(-3) × (-15) = (-3, – 15)
(- 5) x (- 9) = (- 5, – 9)

Therefore, the Negative pair factors are (-1, – 45), (- 3, – 15), (-5, – 9).

### Prime Factors of 45

45 ÷ 3 = 15

15 ÷ 3 =  5

5 ÷  5 = 1

``````  3|  45
--|--------
3|  15
--|--------
5|   5
--|---------
|   1``````

So, 3 x 3 x 5 or 32 x 5 are prime factorization of 45.

### Factor tree of 45

``````               45
/  \
3   15
/  \
3    5``````

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## FAQs

### What are the factors of 45?

Answer: 1, 3, 5, 9,15, 45

### What are the factors of – 45?

Answer:  – 1, – 3, – 5, – 9, – 15, – 45

### What are all the factors of 45

Answer: 1, 3, 5, 9,15, 45, – 1, – 3, – 5, – 9, – 15, – 45.

### What is the factor of 45 in pairs?

Answer: (1, 45), (3, 15), (5, 9)

### What is the Prime factorization of 45?

Answer: 3 x 3 x 5 or 32 x 5