# Factors of 560

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560

#### How to find factors of a number

 1.   Find factors of 560 using Division Method 2.   Find factors of 560 using Prime Factorization 3.   Find factors of 560 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 560

• Divide 560 by 1: 560 ÷ 1 : Remainder = 0
• Divide 560 by 2: 560 ÷ 2 : Remainder = 0
• Divide 560 by 4: 560 ÷ 4 : Remainder = 0
• Divide 560 by 5: 560 ÷ 5 : Remainder = 0
• Divide 560 by 7: 560 ÷ 7 : Remainder = 0
• Divide 560 by 8: 560 ÷ 8 : Remainder = 0
• Divide 560 by 10: 560 ÷ 10 : Remainder = 0
• Divide 560 by 14: 560 ÷ 14 : Remainder = 0
• Divide 560 by 16: 560 ÷ 16 : Remainder = 0
• Divide 560 by 20: 560 ÷ 20 : Remainder = 0
• Divide 560 by 28: 560 ÷ 28 : Remainder = 0
• Divide 560 by 35: 560 ÷ 35 : Remainder = 0
• Divide 560 by 40: 560 ÷ 40 : Remainder = 0
• Divide 560 by 56: 560 ÷ 56 : Remainder = 0
• Divide 560 by 70: 560 ÷ 70 : Remainder = 0
• Divide 560 by 80: 560 ÷ 80 : Remainder = 0
• Divide 560 by 112: 560 ÷ 112 : Remainder = 0
• Divide 560 by 140: 560 ÷ 140 : Remainder = 0
• Divide 560 by 280: 560 ÷ 280 : Remainder = 0
• Divide 560 by 560: 560 ÷ 560 : Remainder = 0

Hence, Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560

#### 2. Steps to find factors of 560 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 560 using the division method, follow these steps:

• Step 1. Start dividing 560 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 560, which is 2. Divide 560 by 2 to obtain the quotient (280).
560 ÷ 2 = 280
• Step 3. Repeat step 1 with the obtained quotient (280).
280 ÷ 2 = 140
140 ÷ 2 = 70
70 ÷ 2 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 560 is, 560 = 2 x 2 x 2 x 2 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 560 as shown below:

So, the prime factorization of 560 is, 560 = 2 x 2 x 2 x 2 x 5 x 7.

#### 3. Find factors of 560 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 560 would be the two numbers which, when multiplied, give 560 as the result.

The following table represents the calculation of factors of 560 in pairs:

Factor Pair Pair Factorization
1 and 560 1 x 560 = 560
2 and 280 2 x 280 = 560
4 and 140 4 x 140 = 560
5 and 112 5 x 112 = 560
7 and 80 7 x 80 = 560
8 and 70 8 x 70 = 560
10 and 56 10 x 56 = 560
14 and 40 14 x 40 = 560
16 and 35 16 x 35 = 560
20 and 28 20 x 28 = 560

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 560. They are called negative pair factors.

Hence, the negative pairs of 560 would be ( -1 , -560 ) , ( -2 , -280 ) , ( -4 , -140 ) , ( -5 , -112 ) , ( -7 , -80 ) , ( -8 , -70 ) , ( -10 , -56 ) , ( -14 , -40 ) , ( -16 , -35 ) and ( -20 , -28 ) .

#### 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. 560 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 560.
• Every number is a factor of zero (0), since 560 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, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 are exact divisors of 560.
• Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560. Each factor divides 560 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 are all less than or equal to 560.

• What two numbers make 560?

Two numbers that make 560 are 2 and 280.

• What is prime factorization of 560?

Prime factorization of 560 is 2 x 2 x 2 x 2 x 5 x 7.

• Write some multiples of 560?

First five multiples of 560 are 1120, 1680, 2240, 2800.

• Which is the smallest prime factor of 560?

The smallest prime factor of 560 is 2.

• Is 560 a perfect square?

No 560 is not a perfect square.

• What is the sum of all factors of 560?

The sum of all factors of 560 is 1488.

• What are factors of 560?

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.

• How do you find factors of a negative number? ( eg. -560 )?

Factors of -560 are -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -35, -40, -56, -70, -80, -112, -140, -280, -560.

• Is 560 a whole number?

Yes 560 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 560. Help him in finding the mean of 560.

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 560 is 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 28 + 35 + 40 + 56 + 70 + 80 + 112 + 140 + 280 + 560 = 1488.
Hence, the mean of factors of 560 is 1488 ÷ 20 = 74.40.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 560? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
Negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -35, -40, -56, -70, -80, -112, -140, -280, -560.

Joey wants to write all the prime factors of 560 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 560 are 2, 2, 2, 2, 5, 7.
So in exponential form it can be written as 24 x 5 x 7.

Kevin has been asked to write 19 factor(s) of 560. Can you predict the answer?

19 factor(s) of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280.

Sammy is puzzled while calculating the prime factors of 560. Can you help him find them?

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
Prime factors of 560 are 2, 2, 2, 2, 5, 7

What is prime factorization of 560?

Prime factorization of 560 is 2 x 2 x 2 x 2 x 5 x 7 = 24 x 5 x 7.

Can you help Rubel to find out the product of the even factors of 560?

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
Even factors of 560 are 2, 4, 8, 10, 14, 16, 20, 28, 40, 56, 70, 80, 112, 140, 280, 560.
Hence, product of even factors of 560 is; 2 x 4 x 8 x 10 x 14 x 16 x 20 x 28 x 40 x 56 x 70 x 80 x 112 x 140 x 280 x 560 = 2.4759631762948096e+24.