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In the world of numbers, Factors of 15 helps simplify fractions, find common denominators, and solve problems that include multiples or divisors of 15. Moreover, they are essential in determining possible combinations in areas like permutations as well as combinations. Read on to learn more about the Factors of 15, by division method, via HCF, their factor pairs and more!
Table of Contents
What are the Factors of 15?
The Factors of 15 are all the whole numbers that are divided into 15 without a remainder. Moreover, here is the list of Factors for 15:
1, 3, 5, and 15
Now, to explain the “why” behind it, you need to know that each of these numbers divides into 15 perfectly:
- 15 divided by 1 equals 15 (no remainder)
- 15 divided by 3 equals 5 (no remainder)
- 15 divided by 5 equals 3 (no remainder)
- 15 divided by 15 equals 1 (no remainder)
Additionally, it is important to note that 1 is a factor of every single whole number. Further, the number itself (in this case, 15) is always considered a factor.
Also Read: All You Need to Know About HCF and LCM
Also Read: 10 Properties of Determinants: Formulas and Examples
Factors of 15 by Division Method
The Factors of 15 by Division Method is when you can one by one try dividing 15 by different whole numbers and see which ones give a whole number result (without a remainder).
- Start with the smallest possible positive divisor, which is 1. Since 15 divided by 1 equals 15 (no remainder), 1 is a Factor of 15.
- Now, on to the next whole number which is 2. Dividing 15 by 2 results in 7.5, which is not a whole number. So, 2 is not a factor of 15.
- Continue this process with 3. Dividing 15 by 3 gives us 5 (a whole number). Therefore, 3 is a Factor of 15.
- Repeat the division with 4, 5, and so on. You will find that 5 divides into 15 with a result of 3, making 5 another Factor of 15.
- Notably, any numbers greater than 15 will not be divided evenly into 15.
Therefore, via the Division Method, you arrive at the same set of factors as before: 1, 3, 5, and 15.
What are the Factors of 15 in HCF?
HCF is the Highest Common Factor and is the largest number that is a factor of two or more given numbers. Furthermore, while this concept is normally used for finding the HCF of multiple numbers, it can be applied to a single number as well. In the case of 15, its HCF with itself is simply itself, which is 15.
Also Read: Cross-Sectional Area of Different Shapes with Formula
Also Read: What is the HCF of Two Consecutive Numbers?
What are Factor Pairs for 15?
Factor pairs are two numbers that, when multiplied together, result in the original number. Since there are four factors of 15 which are 1, 3, 5, and 15, you can create two pairs of factors:
- 1 x 15 = 15
- 3 x 5 = 15
Therefore, each pair has two factors that leads to 15.
Also Read: Algebraic Identities: Examples and Chart
What are the Multiples Factors of 15?
Multiples are the opposite of factors. A multiple of a number is any integer that can be obtained by multiplying that number by a whole number (including 0). While the factors are divided evenly into 15, the multiples are the numbers we get when we multiply the factors by whole numbers.
Moreover, here are some examples of multiples for each Factor of 15:
- Multiples of 1: Every whole number is a multiple of 1, including all the factors and multiples of 15 (1, 2, 3, 4, 5, etc.).
- Multiples of 3: 3, 6, 9, 12, 18, etc. (any number divisible by 3)
- Multiples of 5: 5, 10, 15, 20, 25, etc. (any number divisible by 5)
- Multiples of 15: 15, 30, 45, 60, 75, etc. (any number divisible by 15)
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