# Factors of 960

Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960

#### How to find factors of a number

 1.   Find factors of 960 using Division Method 2.   Find factors of 960 using Prime Factorization 3.   Find factors of 960 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 960

• Divide 960 by 1: 960 ÷ 1 : Remainder = 0
• Divide 960 by 2: 960 ÷ 2 : Remainder = 0
• Divide 960 by 3: 960 ÷ 3 : Remainder = 0
• Divide 960 by 4: 960 ÷ 4 : Remainder = 0
• Divide 960 by 5: 960 ÷ 5 : Remainder = 0
• Divide 960 by 6: 960 ÷ 6 : Remainder = 0
• Divide 960 by 8: 960 ÷ 8 : Remainder = 0
• Divide 960 by 10: 960 ÷ 10 : Remainder = 0
• Divide 960 by 12: 960 ÷ 12 : Remainder = 0
• Divide 960 by 15: 960 ÷ 15 : Remainder = 0
• Divide 960 by 16: 960 ÷ 16 : Remainder = 0
• Divide 960 by 20: 960 ÷ 20 : Remainder = 0
• Divide 960 by 24: 960 ÷ 24 : Remainder = 0
• Divide 960 by 30: 960 ÷ 30 : Remainder = 0
• Divide 960 by 32: 960 ÷ 32 : Remainder = 0
• Divide 960 by 40: 960 ÷ 40 : Remainder = 0
• Divide 960 by 48: 960 ÷ 48 : Remainder = 0
• Divide 960 by 60: 960 ÷ 60 : Remainder = 0
• Divide 960 by 64: 960 ÷ 64 : Remainder = 0
• Divide 960 by 80: 960 ÷ 80 : Remainder = 0
• Divide 960 by 96: 960 ÷ 96 : Remainder = 0
• Divide 960 by 120: 960 ÷ 120 : Remainder = 0
• Divide 960 by 160: 960 ÷ 160 : Remainder = 0
• Divide 960 by 192: 960 ÷ 192 : Remainder = 0
• Divide 960 by 240: 960 ÷ 240 : Remainder = 0
• Divide 960 by 320: 960 ÷ 320 : Remainder = 0
• Divide 960 by 480: 960 ÷ 480 : Remainder = 0
• Divide 960 by 960: 960 ÷ 960 : Remainder = 0

Hence, Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960

#### 2. Steps to find factors of 960 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 960 using the division method, follow these steps:

• Step 1. Start dividing 960 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 960, which is 2. Divide 960 by 2 to obtain the quotient (480).
960 ÷ 2 = 480
• Step 3. Repeat step 1 with the obtained quotient (480).
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 960 is, 960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 960 as shown below:

So, the prime factorization of 960 is, 960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5.

#### 3. Find factors of 960 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 960 would be the two numbers which, when multiplied, give 960 as the result.

The following table represents the calculation of factors of 960 in pairs:

Factor Pair Pair Factorization
1 and 960 1 x 960 = 960
2 and 480 2 x 480 = 960
3 and 320 3 x 320 = 960
4 and 240 4 x 240 = 960
5 and 192 5 x 192 = 960
6 and 160 6 x 160 = 960
8 and 120 8 x 120 = 960
10 and 96 10 x 96 = 960
12 and 80 12 x 80 = 960
15 and 64 15 x 64 = 960
16 and 60 16 x 60 = 960
20 and 48 20 x 48 = 960
24 and 40 24 x 40 = 960
30 and 32 30 x 32 = 960

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 960. They are called negative pair factors.

Hence, the negative pairs of 960 would be ( -1 , -960 ) , ( -2 , -480 ) , ( -3 , -320 ) , ( -4 , -240 ) , ( -5 , -192 ) , ( -6 , -160 ) , ( -8 , -120 ) , ( -10 , -96 ) , ( -12 , -80 ) , ( -15 , -64 ) , ( -16 , -60 ) , ( -20 , -48 ) , ( -24 , -40 ) and ( -30 , -32 ) .

#### 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

• Each number is a factor of itself. Eg. 960 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 960.
• Every number is a factor of zero (0), since 960 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, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 are exact divisors of 960.
• Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960. Each factor divides 960 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 are all less than or equal to 960.

• How do you find factors of a negative number? ( eg. -960 )?

Factors of -960 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -160, -192, -240, -320, -480, -960.

• What is the sum of all factors of 960?

The sum of all factors of 960 is 3048.

• What is prime factorization of 960?

Prime factorization of 960 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5.

• What are the pair factors of 960?

Pair factors of 960 are (1,960), (2,480), (3,320), (4,240), (5,192), (6,160), (8,120), (10,96), (12,80), (15,64), (16,60), (20,48), (24,40), (30,32).

• What are six multiples of 960?

First five multiples of 960 are 1920, 2880, 3840, 4800, 5760, 6720.

• Is 960 a whole number?

Yes 960 is a whole number.

• Which is the smallest prime factor of 960?

Smallest prime factor of 960 is 2.

• What are five multiples of 960?

First five multiples of 960 are 1920, 2880, 3840, 4800, 5760.

• Write all factors of 960?

Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.

#### Examples of Factors

Joey wants to write all the prime factors of 960 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 960 are 2, 2, 2, 2, 2, 2, 3, 5.
So in exponential form it can be written as 26 x 3 x 5.

How many factors are there for 960?

Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
So there are in total 28 factors.

Kevin has been asked to write 27 factor(s) of 960. Can you predict the answer?

27 factor(s) of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480.

Sammy is puzzled while calculating the prime factors of 960. Can you help him find them?

Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
Prime factors of 960 are 2, 2, 2, 2, 2, 2, 3, 5

What is prime factorization of 960?

Prime factorization of 960 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 = 26 x 3 x 5.

Ariel has been assigned the task to find the product of all the prime factors of 960. Can you help her?

Prime factors of 960 are 2, 2, 2, 2, 2, 2, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 960?

Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
Even factors of 960 are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
Hence, product of even factors of 960 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 20 x 24 x 30 x 32 x 40 x 48 x 60 x 64 x 80 x 96 x 120 x 160 x 192 x 240 x 320 x 480 x 960 = 2.509659166022727e+39.