Factors of 15 Using Prime Factorization
Factors of 15
Factors | Factor pairs | Prime factorization |
|---|---|---|
1, 3, 5, 15 | (1, 15), (3, 5) | 15 = 3 × 5 |
What are the factors of 15?
Factors of 15 are natural numbers that divide 15 without leaving any remainder, or in other words, the factors of 15 divide 15 evenly.
Example: 5 is a factor of 15 because when we divide 15 by 5, it gives us 3 as the quotient, and 0 as the remainder. Here the quotient, 3, is also a factor of 15.
So, to check if any number is a factor of 15 or not, divide 15 by that number and verify whether the remainder is zero or not. If the remainder is zero, then the number is a factor of 15.
Factor List of 15
Factors of 15 can be obtained by applying the divisibility rules and division facts.
Number | Is the number a factor of 15? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 15 = 15 |
2 | No, 15 is an odd number 152 = 7 Remainder = 1 | - |
3 | Yes, 1 + 5 = 6 is divisible by 3 | 3 x 5 = 15 |
4 | No, 15 \(\div \) 4 = 3 Remainder = 3 | - |
We can stop checking after 4 as the factor pairs start to repeat.
Hence the factors of 15 are 1, 3, 5 and 15.
Prime Factors of 15
A factor tree can be used to learn about the prime factorization of 15.
From the factor tree we can see prime factorization of 15 is 3 × 5.
This means 3 and 5 are the prime factors of 15.
Factor Pairs of 15
The factor pair of 15 is the combination of two factors of 15 which when multiplied together result in 15.
Example: (3, 5) is the factor pair of 15, as 3 x 5 = 15.
The factor pair can be a positive pair or a negative pair.
Factors pairs of a number can be obtained from the list of factors of the number.
Read More:
Positive Factor Pairs of 15
Positive factors of 15 | Positive Factor Pairs of 15 |
|---|---|
1 × 15 | (1, 15) |
3 × 5 | (3, 5) |
Rapid Recall
Solved Factors of 15 Examples
Example 1: Find the common factors of 60 and 15.
Solution:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 15: 1, 3, 5 and 15.
So, the common factors of 60 and 15 are 1, 3, 5 and 15.
Example 2: What is the greatest common factor of 21 and 15?
Solution:
The factors of 21 are 1, 3, 7 and 21.
The factors of 15 are 1, 3, 5 and 15.
So the common factors of 21 and 15 are 1 and 3.
Hence the greatest common factor of 21 and 15 is 3.
Example 3: How many common factors do 15 and 42 have?
Solution:
The factors of 15 are 1, 3, 5 and 15.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
So the common factors of 15 and 42 are 1 and 3.
Hence 15 and 42 have a total of 2 common factors.
Example 4:
A school library has a collection of 15 books on the history of America. The books are to be arranged evenly on 5 shelves. How many books will be placed on each shelf?
Solution:
15 books are to be evenly arranged on 5 shelves.
To find how many books can be placed on each shelf we will divide 15 by 5, that is,
\(\frac{15}{5}\)
= \(\frac{5~\times~3}{5}\) [(5,3) is a factor pair of 15]
= 3 [Divide both numerator and denominator by 5]
As a result, 3 books can be placed on one shelf.
No, when you divide 15 by 7 it will give us 8 as the remainder, that is, 7 does not divide 15 evenly.
Numbers that divide 15 evenly, that is, leave zero as the remainder are known as factors of 15.
The factors of 15 are 1, 3, 5 and 15.
Hence, the sum of all the factors of 15 is
= 1 + 3 + 5 + 15 = 24
Hence, the sum is 24.
Yes, 15 is a composite number as it has factors other than one and itself. It has factors 3, 5 other than 1 and 15.
The factors of 50 are 1, 3, 5 and 15.
So, the least factor of 15 is 1 and the greatest factor is 15 itself.