Factors

# Factors of 15 | Prime Factorization of 15 | Factor Tree of 15

Written by Prerit Jain

Updated on: 08 Jun 2023

Contents

### Factors of 15 | Prime Factorization of 15 | Factor Tree of 15

## Factors of 15

Factors of 15 | Factor Pairs of 15 | Prime factors of 15 |

1, 3, 5, 15 | (1,15) (3,5) (5,3) | 3 x 5 |

**Factors of 15**,

**Factor Pairs of 15**,

**Prime factors of 15**

Calculate Factors of

**The Factors are**

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## What are the factors of 15

The factors of 15 are the numbers that can be multiplied together to get the number 15. To find the factors of 15, follow these steps:

- Write down the number 15.
- Divide 15 by all the integers from 1 to 15 to find the factors.
- If the remainder is 0 for any of these divisions, then the corresponding numbers are factors of 15.

For example, when we divide 15 by 1, we get a quotient of 15 and a remainder of 0. This means that 1 is a factor of 15. When we divide 15 by 2, we get a quotient of 7 and a remainder of 1, so 2 is not a factor. When we divide 15 by 3, we get a quotient of 5 and a remainder of 0. This means that 3 is a factor of 15. And so on.

**The complete list of factors of 15 is 1, 3, 5, and 15.**

## How to Find Factors of 15

Here is a step-by-step guide on how to find the factors of 15:

- Factor of 15 using Multiplication Method
- Factors of 15 using the Division Method
- Prime Factorization of 15
- Factor tree of 15

## Factors of 15 using Multiplication Method

To find the factors of 15 using the multiplication method, follow these steps:

- Start by writing down the number 15.
- List all the pairs of numbers that can be multiplied together to get 15. These pairs are the factors of 15.

The factors of 15 using the multiplication method are: (1, 15), (3, 5), (5, 3), (15, 1)

Note that the order in which the numbers appear in the pair does not matter, so (1, 15) and (15, 1) are considered the same pair.

Alternatively, you can use the division method to find the factors of 15. To do this, divide 15 by all the integers from 1 to 15 and check the remainder. If the remainder is 0 for any of these divisions, then the corresponding numbers are a factor pair of 15.

## Factors of 15 using the Division Method

Find the factors of 15 using the multiplication method, and follow these steps:

- Write down the number 15.
- List all the pairs of numbers that can be multiplied together to equal 15. The factors of 15 using the multiplication method are: (1, 15), (3, 5), (5, 3), (15, 1)

Note that the order in which the numbers appear in the pair does not matter, so (1, 15) and (15, 1) are considered the same pair.

Alternatively, you can use the division method to find the factors of 15. To do this, divide 15 by all the integers from 1 to 15 and check the remainder. If the remainder is 0 for any of these divisions, then the corresponding numbers are a factor pair of 15.

## Prime Factorization of 15

Calculate Prime Factors of

The Prime Factors of 15 =

3 x

5

The prime factorization of 15 is 3 x 5.

To find the prime factorization of a number, you need to find the prime numbers that can be multiplied together to give the original number. For example, the prime factorization of 15 is 3 x 5, because 3 and 5 are prime numbers and 15 can be expressed as the product of 3 and 5 (3 x 5 = 15).

The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 15 is written as 3 x 5.

## Factor tree of 15

To find the prime factorization of 15 using a factor tree, follow these steps:

- Write down the number 15.
- Find the smallest prime factor of 15. The smallest prime factor of 15 is 3.
- Draw a branch from the number 15 and write the prime factor (3) on the branch.
- Divide the number 15 by 3 to get 5.
- Draw a branch from the number 5 and write the prime factor (5) on the branch.
- The prime factorization of 15 is now complete, so the factor tree is done.

The completed factor tree for 15 looks like this: 5 x 3.

## Factor Pairs of 15

Calculate Pair Factors of

1 x 15=15

3 x 5=15

5 x 3=15

So Pair Factors of 15 are

(1,15)

(3,5)

(5,3)

To find the factor pairs of 15, follow these steps:

- Begin by writing down the number 15.
- Divide 15 by all the integers from 1 to 15 to find the factors.
- If the remainder is 0 for any of these divisions, then the corresponding numbers are a factor pair of 15.

For example, when we divide 15 by 1, we get a quotient of 15 and a remainder of 0. This means that 1 is a factor of 15. When we divide 15 by 2, we get a quotient of 7 and a remainder of 1, so 2 is not a factor. When we divide 15 by 3, we get a quotient of 5 and a remainder of 0. This means that 3 is a factor of 15. And so on.

**The complete list of factor pairs of 15 is: (1, 15), (3, 5), (5, 3), (15, 1)**

Note that the order in which the numbers appear in the pair does not matter, so (1, 15) and (15, 1) are considered the same pair.

## Factors of 15 – Quick Recap

**Factors of 15:**1, 3, 5, and 15.**Negative Factors of 15:**(-1, -15) and (-3, -5).**Prime Factors of 15:**3 and 5**Prime Factorization of 15:**3 × 5

## Factors of 15 – Fun Facts

- 15 is a composite number, which means it has more than two factors. The factors of 15 are 1, 3, 5, and 15.
- 15 is the smallest triangular number, meaning it is the smallest number that can be represented as the sum of consecutive integers starting from 1. The triangular numbers are 1,2,3,4,5.
- 15 is the smallest multiple of three that is greater than 10.
- 15 is the lowest common multiple (LCM) of 3 and 5. The LCM of two numbers is the smallest number that is a multiple of both numbers.
- 15 is the sum of the first four positive integers (1+2+3+4).
- 15 is the product of the first three prime numbers (2 x 3 x 5).
- 15 is the number of minutes in one-quarter of an hour.
- 15 is the number of days in the shortest month of the year (February).
- 15 is the atomic number of phosphorus, an element that is essential for the growth and repair of tissues in the human body.
- 15 is a number that appears frequently in popular culture and literature. For example, it is the number of players on a football team, the age at which a person becomes a “quinceañera” in Latin American culture, and the number of beads in a traditional Catholic rosary.

Also Check: Multiples, Square Root, and LCM

## Solved Examples of Factor of 15

**Q.1: Divide 210 by a factor of 15 and explain your answer using division terms. ** **Solution: **210 divided by 15 is 14, so the answer is 14 with no remainder.

**Q.2:** What is the prime factorization of 135?**Solution: **The prime factorization of 135 is 3 x 3 x 3 x 5.

** Q.3:Write 3 five-digit numbers with a factor of 15 in each one. Solution: **15,315; 64515; 330015

**Q.4:** Find three multiples of 15 that add to the number 90. **Solution: **45 + 30 + 15 = 90

** Q.5:A factory produces 60 units of a product every day. How many units will be produced in 45 days? Solution: **60 x 45 = 2,700 units will be produced in 45 days

**Q.6:**How many equal shares can Sam give if she has 30 items and each person gets a factor of 15? **Solution: **Sam can give two equal shares to each person as 30 divided by 15 is 2 (with no remainder).

** Q.7: Evan needs to buy enough snacks for his classmates but he only has $45; what is the maximum amount he can spend per student if each student receives a factor of 15?Solution: ** Evan can spend up to $3 per student as 45 divided by 15 is 3 (with no remainder).

**Q.8:** What is the least common multiple between 24 and 30?

**Solution: **The least common multiple between 24 and 30 is 120 (LCM = 24 x 5 = 120).

**Q.9:** A certain number when divided by 15 leaves a remainder of 11, what is the number?**Solution: **The number is 166 (166 ÷ 15 = 11 with 1 remainder).

**Q.10:** What two numbers multiplied together will result in 225?**Solution: **Two numbers that when multiplied together will result in 225 are 9 and 25 (9 x 25 = 225).

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## Frequently Asked Questions on Factors of 15

**What are the factors of 15?**

The factors of 15 are 1, 3, 5, and 15.

**How many factors does the number 15 have?**

The number 15 has 4 factors which are 1, 3, 5, and 15.

**Is 15 a prime number?**

No, 15 is not a prime number because it can be divided evenly by more than two numbers (1, 3, 5, and 15).

**What is the greatest common factor of 12 and 15?**

The greatest common factor of 12 and 15 is 3.

**What is the least common multiple between 24 and 30?**

The least common multiple between 24 and 30 is 120 (LCM = 24 x 5 = 120).

**Can you divide 210 by a factor of 15?**

Yes, you can divide 210 by a factor of 15; the answer would be 14 with no remainder.

**How do you find multiples of a given number such as 15?**

To find multiples of any given number such as 15, multiply it by any positive integer (i.e., 1×15 =15; 2×15 =30; 3×15=45, etc.).

**What two numbers multiplied together will result in 225?**

Two numbers that multiplied together will result in 225 are 9 and 25 (9 x 25 = 225).

**A certain number when divided by 15 leaves a remainder of 11, what is the number?**

The number is 166 (166 ÷ 15 = 11 with 1 remainder).

**How many equal shares can Sam give if she has 30 items and each person gets a factor of 15?**

Sam can give two equal shares to each person as 30 divided by 15 is 2 (with no remainder).

Written by by

Prerit Jain