Factors of 45
Factors of 45 are integers that can be divided evenly into 45. There are a total of 6 factors of 45 i.e. 1, 3, 5, 9, 15, and 45. The sum of all factors of 45 is 78. Its Prime Factors are 1, 3, 5, 9, 15, 45, and (1, 45), (3, 15) and (5, 9) are Pair Factors.
 Factors of 45: 1, 3, 5, 9, 15 and 45
 Negative Factors of 45: 1, 3, 5, 9, 15 and 45
 Prime Factors of 45: 3, 5
 Prime Factorization of 45: 3 × 3 × 5 = 3^{2} × 5
 Sum of Factors of 45: 78
1.  What are Factors of 45? 
2.  How to Calculate Factors of 45? 
3.  Factors of 45 by Prime Factorization 
4.  Factors of 45 in Pairs 
5.  Important Notes 
6.  FAQs on Factors of 45 
What are the Factors of 45?
Factors of a number n are the numbers that completely divide the number n. It means that if the remainder in n/a is zero, then a is the factor of n.
We are talking here about factors of the number 45. Let's first see the numbers that completely divide 45.
 45 ÷ 3 = 15
 45 ÷ 5 = 9
 45 ÷ 45 = 1
The numbers that divide 45 completely are:
How to Calculate the Factors of 45?
Factors of any number n can be calculated by many methods. One of the methods is dividing the number by the smallest of the factors. Factors of the number 45 can be calculated as follows:
 Step 1: Write the two smallest factors of 45 (except 1).
 Step 2: The two smallest factors of 45 are 3 and 5.
 Step 3: Divide 45 by 3 and 5 i.e. 45 ÷ 3 = 15 and 45 ÷ 5 = 9
 Step 4: So, 3, 5, 9, and 15 are the factors of 45.
 Step 5: Repeat step 2 as long as we are getting new factors. For 45, these are the only factors.
 Step 6: Include 1 and the number itself to the factors.
Hence, the factors of 45 are 1, 3, 5, 9, 15, and 45. Explore factors using illustrations and interactive examples:
 Factors of 175  The factors of 175 are 1, 5, 7, 25, 35, 175
 Factors of 15  The factors of 15 are 1, 3, 5, 15
 Factors of 25  The factors of 25 are 1, 5, 25
 Factors of 35  The factors of 35 are 1, 5, 7, 35
 Factors of 63  The factors of 63 are 1, 3, 7, 9, 21, 63
 Factors of 54  The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
Factors of 45 by Prime Factorization
The prime factorization method to calculate factors of any number is one of the most important methods. Many students prefer using prime factorization while performing calculations. In the prime factorization method, we can only factorize a number into its prime factors.
Prime Numbers
Prime numbers are the numbers that have only two factors, 1 and the number itself. Examples of prime numbers: 2, 3, 5, 7, 11, 13, and so on.
Prime factors of 45 are 45 = 3 × 3 × 5 . Let's write all the factors of 45 using prime factors:
 Step 1: Take all the numbers once: 3, 5
 Step 2: Multiply each number with another number, once.
3 × 3 = 9
3 × 5 = 15
Factors obtained are 9 and 15.  Step 3: Write all the factors of the number.
Factors of 45: 1, 3, 5, 9, 15, 45
Now that we have done prime factorization of 45, we can multiply it and get the other factors. Can you try and find out if all the factors are covered or not? As you might have already guessed, for prime numbers, there are no other factors.
Factors of 45 in Pairs
The pair of factors of a number n is the set of two numbers which, when multiplied together, give the number n.
Factors of 45 are: 1, 3, 5, 9, 15, 45. Factors of 45 in pair are: (1, 45), (3, 15), (5, 9)
 1 × 45 = 45
 3 × 15 = 45
 5 × 9 = 45
Negative factor pairs of 45 are: (1, 45), (3, 15), (5, 9)
 1 × 45 = 45
 3 × 15 = 45
 5 × 9 = 45
Important Notes:
 All the factors of 45 are 1, 3, 5, 9, 15, and 45.
 Prime factorization of 45 is 45 = 3^{2} × 5.
 There are no factors of a number n between (n, n/2).
 Factors of 45 in pair are: (1, 45), (3, 15), (5, 9).
Factors of 45 Solved Examples

Example 1: John wants to distribute 45 apples and 75 bananas to his friends. What is the maximum number of friends he should distribute the fruits to so that everyone gets an equal number of apples and bananas?
Solution:
John has 45 apples and 75 bananas.
To find the maximum number of friends he needs to invite, we need to calculate the HCF of 45 and 75.
45 = 1 × 3 × 3 × 5
75 = 1 × 3 × 5 × 5
HCF of 45 and 75 = 3 × 5 = 15. Hence, John should invite 15 friends. Each friend will get 3 apples and 5 bananas.

Example 2: Find the prime factors of 45.
Solution:
We know that all the factors of 45 are 1, 3, 5, 9, 15, and 45. A prime number that is not a composite number is a prime factor.
Prime factorization of 45 = 1 × 3 × 3 × 5. Therefore, Prime factors of 45 are 1, 3, and 5.

Example 3: Find the product of all the prime factors of 45.
Solution:
Since, the prime factors of 45 are 3, 5. Therefore, the product of prime factors = 3 × 5 = 15.

FAQs on Factors of 45
What are the Factors of 45?
The factors of 45 are 1, 3, 5, 9, 15, 45 and its negative factors are 1, 3, 5, 9, 15, 45.
What are the Pair Factors of 45?
The pair factors of 45 are (1, 45), (3, 15), (5, 9).
How Many Factors of 28 are also common to the Factors of 45?
Since, the factors of 45 are 1, 3, 5, 9, 15, 45, and factors of 28 are 1, 2, 4, 7, 14, 28. Hence, 45 and 28 have only one common factor which is 1. Therefore, 45 and 28 are coprime.
What is the Sum of all the Factors of 45?
Factors of 45 are 1, 3, 5, 9, 15, 45 and, the sum of all these factors is 1 + 3 + 5 + 9 + 15 + 45 = 78
What is the Greatest Common Factor of 45 and 40?
The factors of 45 and 40 are 1, 3, 5, 9, 15, 45 and 1, 2, 4, 5, 8, 10, 20, 40 respectively.
Common factors of 45 and 40 are [1, 5].
Hence, the Greatest Common Factor of 45 and 40 is 5.
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