# Factors of 945

Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945

#### How to find factors of a number

 1.   Find factors of 945 using Division Method 2.   Find factors of 945 using Prime Factorization 3.   Find factors of 945 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 945

• Divide 945 by 1: 945 ÷ 1 : Remainder = 0
• Divide 945 by 3: 945 ÷ 3 : Remainder = 0
• Divide 945 by 5: 945 ÷ 5 : Remainder = 0
• Divide 945 by 7: 945 ÷ 7 : Remainder = 0
• Divide 945 by 9: 945 ÷ 9 : Remainder = 0
• Divide 945 by 15: 945 ÷ 15 : Remainder = 0
• Divide 945 by 21: 945 ÷ 21 : Remainder = 0
• Divide 945 by 27: 945 ÷ 27 : Remainder = 0
• Divide 945 by 35: 945 ÷ 35 : Remainder = 0
• Divide 945 by 45: 945 ÷ 45 : Remainder = 0
• Divide 945 by 63: 945 ÷ 63 : Remainder = 0
• Divide 945 by 105: 945 ÷ 105 : Remainder = 0
• Divide 945 by 135: 945 ÷ 135 : Remainder = 0
• Divide 945 by 189: 945 ÷ 189 : Remainder = 0
• Divide 945 by 315: 945 ÷ 315 : Remainder = 0
• Divide 945 by 945: 945 ÷ 945 : Remainder = 0

Hence, Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945

#### 2. Steps to find factors of 945 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 945 using the division method, follow these steps:

• Step 1. Start dividing 945 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 945, which is 3. Divide 945 by 3 to obtain the quotient (315).
945 ÷ 3 = 315
• Step 3. Repeat step 1 with the obtained quotient (315).
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 945 is, 945 = 3 x 3 x 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 945 as shown below:

So, the prime factorization of 945 is, 945 = 3 x 3 x 3 x 5 x 7.

#### 3. Find factors of 945 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 945 would be the two numbers which, when multiplied, give 945 as the result.

The following table represents the calculation of factors of 945 in pairs:

Factor Pair Pair Factorization
1 and 945 1 x 945 = 945
3 and 315 3 x 315 = 945
5 and 189 5 x 189 = 945
7 and 135 7 x 135 = 945
9 and 105 9 x 105 = 945
15 and 63 15 x 63 = 945
21 and 45 21 x 45 = 945
27 and 35 27 x 35 = 945

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 945. They are called negative pair factors.

Hence, the negative pairs of 945 would be ( -1 , -945 ) , ( -3 , -315 ) , ( -5 , -189 ) , ( -7 , -135 ) , ( -9 , -105 ) , ( -15 , -63 ) , ( -21 , -45 ) and ( -27 , -35 ) .

#### 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 factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945 are exact divisors of 945.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 945 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 945.

• Which is the smallest prime factor of 945?

Smallest prime factor of 945 is 3.

• Is 945 a perfect square?

No 945 is not a perfect square.

• What are five multiples of 945?

First five multiples of 945 are 1890, 2835, 3780, 4725, 5670.

• What is prime factorization of 945?

Prime factorization of 945 is 3 x 3 x 3 x 5 x 7.

• What are factors of 945?

Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.

• How do you find factors of a negative number? ( eg. -945 )?

Factors of -945 are -1, -3, -5, -7, -9, -15, -21, -27, -35, -45, -63, -105, -135, -189, -315, -945.

• Is 945 a whole number?

Yes 945 is a whole number.

• Which is greatest factor of 945?

The greatest factor of 945 is 315.

• What are the prime factors of 945?

The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.
Prime factors of 945 are 3, 3, 3, 5, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 945. Can you help her?

Prime factors of 945 are 3, 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 945?

Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.
Even factors of 945 are 0.
Hence, product of even factors of 945 is; 0 = 0.

Joy wants to calculate mean of all the factors of 945. Help him in finding the mean of 945.

Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 945 is 1 + 3 + 5 + 7 + 9 + 15 + 21 + 27 + 35 + 45 + 63 + 105 + 135 + 189 + 315 + 945 = 1920.
Hence, the mean of factors of 945 is 1920 ÷ 16 = 120.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 945? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.
Negative factors are -1, -3, -5, -7, -9, -15, -21, -27, -35, -45, -63, -105, -135, -189, -315, -945.

How many factors are there for 945?

Factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945.
So there are in total 16 factors.

Joey wants to write all the prime factors of 945 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 945 are 3, 3, 3, 5, 7.
So in exponential form it can be written as 33 x 5 x 7.

Kevin has been asked to write 15 factor(s) of 945. Can you predict the answer?

15 factor(s) of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315.