Definition of factors of 45: If a number completely divides 45 with the remainder zero, then that number is called a factor of 45. Thus we can say that the factors of 45 are the divisors of 45. In this section, we will learn about the factors of 45 and the prime factors of 45.
Table of Contents
Highlights of Factors of 45
- 45=3×3×5 is the prime factorization of 45.
- The factors of 45 are 1, 3, 5, 9, 15, and 45.
- Prime factors of 45 are 3 and 5.
- Negative factors of 45 are –1, -3, -5, -9, -15, and –45.
What are the factors of 45?
Let us write the number 45 multiplicatively in all possible ways. Doing so we have:
45 = 1×45
45 = 3×15
45 = 5×9
As we can express 45 multiplicatively in no other way, so we will stop right now. So the factors of 45 in pairs are given as follows:
| 45 = a×b | Factors in Pairs (a,b) |
| 45 = 1×45 | (1, 45) |
| 45 = 3×15 | (3, 15) |
| 45 = 5×9 | (5, 9) |
Thus the pair factors of 45 are (1, 45), (3, 15), and (5, 9). As all the numbers appearing in pair factors are the factors of 45, we conclude that
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The factors of 45 are: 1, 3, 5, 9, 15, and 45. |
Number of Factors of 45
From above we have calculated the factors of 45 which are 1, 3, 5, 9, 15, and 45. Thus the total number of factors of 45 is six.
Prime Factors of 45
Note that the factors of 45 are 1, 3, 5, 9, 15, and 45. Among those factors, we notice that only 3 and 5 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 45 are 3 and 5.
Question: What are the factors of 45?
Video Solution:
How to Find Factors of 45?
Now we will determine the factors of 45 by division method. In this method, we will find the numbers that can divide 45 with no remainder. See that
| 45/1=45 and the remainder is 0 | ∴ 1 and 45 are factors of 45 |
| 45/3=15 and the remainder is 0 | ∴ 3 and 15 are factors of 45 |
| 45/5=9 and the remainder is 0 | ∴ 5 and 9 are factors of 45 |
Note that no numbers other than the numbers in violet color can divide 45. So the numbers in violet color, that is, 1, 3, 5, 9, 15, and 45 are the complete list of factors of 45.
