# Factors of 315

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315

#### How to find factors of a number

 1.   Find factors of 315 using Division Method 2.   Find factors of 315 using Prime Factorization 3.   Find factors of 315 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 315

• Divide 315 by 1: 315 ÷ 1 : Remainder = 0
• Divide 315 by 3: 315 ÷ 3 : Remainder = 0
• Divide 315 by 5: 315 ÷ 5 : Remainder = 0
• Divide 315 by 7: 315 ÷ 7 : Remainder = 0
• Divide 315 by 9: 315 ÷ 9 : Remainder = 0
• Divide 315 by 15: 315 ÷ 15 : Remainder = 0
• Divide 315 by 21: 315 ÷ 21 : Remainder = 0
• Divide 315 by 35: 315 ÷ 35 : Remainder = 0
• Divide 315 by 45: 315 ÷ 45 : Remainder = 0
• Divide 315 by 63: 315 ÷ 63 : Remainder = 0
• Divide 315 by 105: 315 ÷ 105 : Remainder = 0
• Divide 315 by 315: 315 ÷ 315 : Remainder = 0

Hence, Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315

#### 2. Steps to find factors of 315 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 315 using the division method, follow these steps:

• Step 1. Start dividing 315 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 315, which is 3. Divide 315 by 3 to obtain the quotient (105).
315 ÷ 3 = 105
• Step 3. Repeat step 1 with the obtained quotient (105).
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 315 is, 315 = 3 x 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 315 as shown below:

So, the prime factorization of 315 is, 315 = 3 x 3 x 5 x 7.

#### 3. Find factors of 315 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 315 would be the two numbers which, when multiplied, give 315 as the result.

The following table represents the calculation of factors of 315 in pairs:

Factor Pair Pair Factorization
1 and 315 1 x 315 = 315
3 and 105 3 x 105 = 315
5 and 63 5 x 63 = 315
7 and 45 7 x 45 = 315
9 and 35 9 x 35 = 315
15 and 21 15 x 21 = 315

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 315. They are called negative pair factors.

Hence, the negative pairs of 315 would be ( -1 , -315 ) , ( -3 , -105 ) , ( -5 , -63 ) , ( -7 , -45 ) , ( -9 , -35 ) and ( -15 , -21 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 315 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315 are exact divisors of 315.
• Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Each factor divides 315 without leaving a remainder.

• Which is the smallest prime factor of 315?

Smallest prime factor of 315 is 3.

• Is 315 a perfect square?

No 315 is not a perfect square.

• What are five multiples of 315?

First five multiples of 315 are 630, 945, 1260, 1575, 1890.

• What is prime factorization of 315?

Prime factorization of 315 is 3 x 3 x 5 x 7.

• What are factors of 315?

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.

• How do you find factors of a negative number? ( eg. -315 )?

Factors of -315 are -1, -3, -5, -7, -9, -15, -21, -35, -45, -63, -105, -315.

• Is 315 a whole number?

Yes 315 is a whole number.

• Which is greatest factor of 315?

The greatest factor of 315 is 105.

• What are the prime factors of 315?

The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
Prime factors of 315 are 3, 3, 5, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 315. Can you help her?

Prime factors of 315 are 3, 3, 5, 7.
Hence, the product of prime factors of 105.

Can you help Rubel to find out the product of the even factors of 315?

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
Even factors of 315 are 0.
Hence, product of even factors of 315 is; 0 = 0.

Joy wants to calculate mean of all the factors of 315. Help him in finding the mean of 315.

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 315 is 1 + 3 + 5 + 7 + 9 + 15 + 21 + 35 + 45 + 63 + 105 + 315 = 624.
Hence, the mean of factors of 315 is 624 ÷ 12 = 52.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 315? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
Negative factors are -1, -3, -5, -7, -9, -15, -21, -35, -45, -63, -105, -315.

How many factors are there for 315?

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
So there are in total 12 factors.

Joey wants to write all the prime factors of 315 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 315 are 3, 3, 5, 7.
So in exponential form it can be written as 32 x 5 x 7.

Kevin has been asked to write 11 factor(s) of 315. Can you predict the answer?

11 factor(s) of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105.