# Factors of 1120

Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, and 1120

#### How to find factors of a number

 1.   Find factors of 1120 using Division Method 2.   Find factors of 1120 using Prime Factorization 3.   Find factors of 1120 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1120

• Divide 1120 by 1: 1120 ÷ 1 : Remainder = 0
• Divide 1120 by 2: 1120 ÷ 2 : Remainder = 0
• Divide 1120 by 4: 1120 ÷ 4 : Remainder = 0
• Divide 1120 by 5: 1120 ÷ 5 : Remainder = 0
• Divide 1120 by 7: 1120 ÷ 7 : Remainder = 0
• Divide 1120 by 8: 1120 ÷ 8 : Remainder = 0
• Divide 1120 by 10: 1120 ÷ 10 : Remainder = 0
• Divide 1120 by 14: 1120 ÷ 14 : Remainder = 0
• Divide 1120 by 16: 1120 ÷ 16 : Remainder = 0
• Divide 1120 by 20: 1120 ÷ 20 : Remainder = 0
• Divide 1120 by 28: 1120 ÷ 28 : Remainder = 0
• Divide 1120 by 32: 1120 ÷ 32 : Remainder = 0
• Divide 1120 by 35: 1120 ÷ 35 : Remainder = 0
• Divide 1120 by 40: 1120 ÷ 40 : Remainder = 0
• Divide 1120 by 56: 1120 ÷ 56 : Remainder = 0
• Divide 1120 by 70: 1120 ÷ 70 : Remainder = 0
• Divide 1120 by 80: 1120 ÷ 80 : Remainder = 0
• Divide 1120 by 112: 1120 ÷ 112 : Remainder = 0
• Divide 1120 by 140: 1120 ÷ 140 : Remainder = 0
• Divide 1120 by 160: 1120 ÷ 160 : Remainder = 0
• Divide 1120 by 224: 1120 ÷ 224 : Remainder = 0
• Divide 1120 by 280: 1120 ÷ 280 : Remainder = 0
• Divide 1120 by 560: 1120 ÷ 560 : Remainder = 0
• Divide 1120 by 1120: 1120 ÷ 1120 : Remainder = 0

Hence, Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, and 1120

#### 2. Steps to find factors of 1120 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 1120 using the division method, follow these steps:

• Step 1. Start dividing 1120 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 1120, which is 2. Divide 1120 by 2 to obtain the quotient (560).
1120 ÷ 2 = 560
• Step 3. Repeat step 1 with the obtained quotient (560).
560 ÷ 2 = 280
280 ÷ 2 = 140
140 ÷ 2 = 70
70 ÷ 2 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 1120 is, 1120 = 2 x 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 1120 as shown below:

So, the prime factorization of 1120 is, 1120 = 2 x 2 x 2 x 2 x 2 x 5 x 7.

#### 3. Find factors of 1120 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 1120 would be the two numbers which, when multiplied, give 1120 as the result.

The following table represents the calculation of factors of 1120 in pairs:

Factor Pair Pair Factorization
1 and 1120 1 x 1120 = 1120
2 and 560 2 x 560 = 1120
4 and 280 4 x 280 = 1120
5 and 224 5 x 224 = 1120
7 and 160 7 x 160 = 1120
8 and 140 8 x 140 = 1120
10 and 112 10 x 112 = 1120
14 and 80 14 x 80 = 1120
16 and 70 16 x 70 = 1120
20 and 56 20 x 56 = 1120
28 and 40 28 x 40 = 1120
32 and 35 32 x 35 = 1120

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 1120. They are called negative pair factors.

Hence, the negative pairs of 1120 would be ( -1 , -1120 ) , ( -2 , -560 ) , ( -4 , -280 ) , ( -5 , -224 ) , ( -7 , -160 ) , ( -8 , -140 ) , ( -10 , -112 ) , ( -14 , -80 ) , ( -16 , -70 ) , ( -20 , -56 ) , ( -28 , -40 ) and ( -32 , -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

• Each number is a factor of itself. Eg. 1120 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1120.
• Every number is a factor of zero (0), since 1120 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, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120 are exact divisors of 1120.
• Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120. Each factor divides 1120 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, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120 are all less than or equal to 1120.

• Is 1120 a perfect square?

No 1120 is not a perfect square.

• What are factors of 1120?

Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120.

• Which is greatest factor of 1120?

The greatest factor of 1120 is 560.

• What is the sum of all factors of 1120?

The sum of all factors of 1120 is 3024.

• What are multiples of 1120?

First five multiples of 1120 are 2240, 3360, 4480, 5600.

• What is the greatest prime factors of 1120?

The greatest prime factor of 1120 is 7.

• What are six multiples of 1120?

First five multiples of 1120 are 2240, 3360, 4480, 5600, 6720, 7840.

• What is prime factorization of 1120?

Prime factorization of 1120 is 2 x 2 x 2 x 2 x 2 x 5 x 7.

• Is 1120 a whole number?

Yes 1120 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1120? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120.
Negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -32, -35, -40, -56, -70, -80, -112, -140, -160, -224, -280, -560, -1120.

Can you help Sammy find out the product of the odd factors of 1120?

Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120.
Odd factors of 1120 are 1, 5, 7, 35.
Hence product of odd factors of 1120 is; 1 x 5 x 7 x 35 = 1225.

Joey wants to write all the prime factors of 1120 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1120 are 2, 2, 2, 2, 2, 5, 7.
So in exponential form it can be written as 25 x 5 x 7.

How many factors are there for 1120?

Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1120. Can you predict the answer?

23 factor(s) of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560.

Sammy is puzzled while calculating the prime factors of 1120. Can you help him find them?

Factors of 1120 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 1120.
Prime factors of 1120 are 2, 2, 2, 2, 2, 5, 7

What is prime factorization of 1120?

Prime factorization of 1120 is 2 x 2 x 2 x 2 x 2 x 5 x 7 = 25 x 5 x 7.