Factors of 450
Factors of 450 are the collection of positive and negative numbers that can be divided evenly into 450. Factors with the negative signs are just negative factors of 450. In this lesson, we will calculate the factors of 450, its prime factors, and its factors in pairs. We will also solve some examples for better understanding.
- Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
- Factors of -450: -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -30, -45, -50, -75, -90, -150, -225, and -450.
- Prime Factorization of 450: 450 = 2 × 3² × 5²
What are Factors of 450?
The factors of 450 will be any number which on dividing 450 leaves no remainder. Since 450 is a composite number, it will have more than two factors.
Factors of 450 are = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
How to Calculate the Factors of 450?
Let us calculate factors of 450. In considering numbers that can divide 450 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, etc up to 225 (which is exactly the half of 450).
| 450/1 gives remainder 0 | 1 is a factor |
| 450/2 gives remainder 0 | 2 is a factor |
| 450/3 gives remainder 0 | 3 is a factor |
| 450/5 gives remainder 0 | 5 is a factor |
| 450/6 gives remainder 0 | 6 is a factor |
| 450/9 gives remainder 0 | 9 is a factor |
| 450/10 gives remainder 0 | 10 is a factor |
| 450/15 gives remainder 0 | 15 is a factor |
| 450/18 gives remainder 0 | 18 is a factor |
| 450/25 gives remainder 0 | 25 is a factor |
| 450/30 gives remainder 0 | 30 is a factor |
| 450/45 gives remainder 0 | 45 is a factor |
| 450/50 gives remainder 0 | 50 is a factor |
| 450/75 gives remainder 0 | 75 is a factor |
| 450/90 gives remainder 0 | 90 is a factor |
| 450/150 gives remainder 0 | 150 is a factor |
| 450/225 gives remainder 0 | 225 is a factor |
| 450/450 gives remainder 0 | 450 is a factor |
Factors of 450 by Prime Factorization
Prime factorization of a number refers to representing a number in the form of products of its prime factors. Prime factors of any number can be found out by the following methods:
Method 1: Division method
Now let us find the prime factors of 450 by division method. Divide the number 450 with the smallest prime number, i.e. 2:
- 450 ÷ 2 = 225
Again, divide 225 by 2:
- 225 ÷ 2 = 112.5
This can not be a factor, so moving to the next prime number.
- 225 ÷ 3 = 75
Again, divide 75 by 3:
- 75 ÷ 3 = 25
Now, if we divide 25 by 3 we get a fraction number, which cannot be a factor. Now, proceed to the next prime numbers, i.e. 5.
- 25 ÷ 5 = 5
Again, divide 5 by 5:
- 5 ÷ 5 = 1
We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorization of 450 is, 2 × 3 × 3 × 5 × 5 or 2 × 32 × 52 where, 2, 3, and 5 are the prime numbers.
Method 2: Factor tree
We will do this by factor tree:
So the prime factorization of 450 is: 450 = 2 × 32 × 52.
Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. The total factors can be written including both the prime and composite numbers together as, 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. Explore factors using illustrations and interactive examples:
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Challenging Question:
- If you are given the prime factorization of a composite number as, X = 2 × 32 × 5. Can you find out the total number of factors of X?
Factors of 450 in Pairs
Pair factors of the number 450 are whole numbers that multiply to get the original number i.e., 450. Pair factors could be either positive or negative but not a fraction or decimal number. There are 18 pair factors of 450 and they are as follows:
| Negative factors Pair | Positive factors Pair |
| -1 × -450= 450 | 1 × 450= 450 |
| -2 × -225= 450 | 2 × 225= 450 |
| -3 × -150= 450 | 3 × 150= 450 |
| -5 × -90= 450 | 5 × 90= 450 |
| -6 × -75= 450 | 6 × 75= 450 |
| -9 × -50= 450 | 9 × 50= 450 |
| -10 × -45= 450 | 10 × 45= 450 |
| -15 × -30= 450 | 15 × 30= 450 |
| -18 × -25= 450 | 18 × 25= 450 |
| -25 × -18= 450 | 25 × 18= 450 |
Important Notes:
- Only whole numbers and integers can be converted to factors.
- Only composite numbers can have more than two factors.
- The smallest factor of a number is 1 and the largest factor of a number would be the number itself.
FAQs on Factors of 450
What are the Prime Factors of 450?
The factors of 450 are, 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. The prime factors among all the factors of 450 are, 1, 2, 3 and 5.
What are all the Positive Pair Factors of 450?
Positive pair factors of 450 are:
- 1 × 450= 450
- 2 × 225= 450
- 3 × 150= 450
- 5 × 90= 450
- 6 × 75= 450
- 9 × 50= 450
- 10 × 45= 450
- 15 × 30= 450
- 18 × 25= 450
- 25 × 18= 450
What are the Factors of 450?
Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
What are all the Negative Pair Factors of 450?
All the negative pair factors of 450 are:
- -1 × -450= 450
- -2 × -225= 450
- -3 × -150= 450
- -5 × -90= 450
- -6 × -75= 450
- -9 × -50= 450
- -10 × -45= 450
- -15 × -30= 450
- -18 × -25= 450
- -25 × -18= 450
How many Factors of 450 are there?
Factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. There are total 18 factors of 450.