# Factors of 1100

Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, and 1100

#### How to find factors of a number

 1.   Find factors of 1100 using Division Method 2.   Find factors of 1100 using Prime Factorization 3.   Find factors of 1100 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1100

• Divide 1100 by 1: 1100 ÷ 1 : Remainder = 0
• Divide 1100 by 2: 1100 ÷ 2 : Remainder = 0
• Divide 1100 by 4: 1100 ÷ 4 : Remainder = 0
• Divide 1100 by 5: 1100 ÷ 5 : Remainder = 0
• Divide 1100 by 10: 1100 ÷ 10 : Remainder = 0
• Divide 1100 by 11: 1100 ÷ 11 : Remainder = 0
• Divide 1100 by 20: 1100 ÷ 20 : Remainder = 0
• Divide 1100 by 22: 1100 ÷ 22 : Remainder = 0
• Divide 1100 by 25: 1100 ÷ 25 : Remainder = 0
• Divide 1100 by 44: 1100 ÷ 44 : Remainder = 0
• Divide 1100 by 50: 1100 ÷ 50 : Remainder = 0
• Divide 1100 by 55: 1100 ÷ 55 : Remainder = 0
• Divide 1100 by 100: 1100 ÷ 100 : Remainder = 0
• Divide 1100 by 110: 1100 ÷ 110 : Remainder = 0
• Divide 1100 by 220: 1100 ÷ 220 : Remainder = 0
• Divide 1100 by 275: 1100 ÷ 275 : Remainder = 0
• Divide 1100 by 550: 1100 ÷ 550 : Remainder = 0
• Divide 1100 by 1100: 1100 ÷ 1100 : Remainder = 0

Hence, Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, and 1100

#### 2. Steps to find factors of 1100 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 1100 using the division method, follow these steps:

• Step 1. Start dividing 1100 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 1100, which is 2. Divide 1100 by 2 to obtain the quotient (550).
1100 ÷ 2 = 550
• Step 3. Repeat step 1 with the obtained quotient (550).
550 ÷ 2 = 275
275 ÷ 5 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1

So, the prime factorization of 1100 is, 1100 = 2 x 2 x 5 x 5 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1100 as shown below:

So, the prime factorization of 1100 is, 1100 = 2 x 2 x 5 x 5 x 11.

#### 3. Find factors of 1100 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 1100 would be the two numbers which, when multiplied, give 1100 as the result.

The following table represents the calculation of factors of 1100 in pairs:

Factor Pair Pair Factorization
1 and 1100 1 x 1100 = 1100
2 and 550 2 x 550 = 1100
4 and 275 4 x 275 = 1100
5 and 220 5 x 220 = 1100
10 and 110 10 x 110 = 1100
11 and 100 11 x 100 = 1100
20 and 55 20 x 55 = 1100
22 and 50 22 x 50 = 1100
25 and 44 25 x 44 = 1100

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 1100. They are called negative pair factors.

Hence, the negative pairs of 1100 would be ( -1 , -1100 ) , ( -2 , -550 ) , ( -4 , -275 ) , ( -5 , -220 ) , ( -10 , -110 ) , ( -11 , -100 ) , ( -20 , -55 ) , ( -22 , -50 ) and ( -25 , -44 ) .

#### 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. 1100 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1100.
• Every number is a factor of zero (0), since 1100 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, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 are exact divisors of 1100.
• Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100. Each factor divides 1100 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 are all less than or equal to 1100.

• What two numbers make 1100?

Two numbers that make 1100 are 2 and 550.

• What is prime factorization of 1100?

Prime factorization of 1100 is 2 x 2 x 5 x 5 x 11.

• Write some multiples of 1100?

First five multiples of 1100 are 2200, 3300, 4400, 5500.

• Which is the smallest prime factor of 1100?

The smallest prime factor of 1100 is 2.

• Is 1100 a perfect square?

No 1100 is not a perfect square.

• What is the sum of all factors of 1100?

The sum of all factors of 1100 is 2604.

• What are factors of 1100?

Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.

• How do you find factors of a negative number? ( eg. -1100 )?

Factors of -1100 are -1, -2, -4, -5, -10, -11, -20, -22, -25, -44, -50, -55, -100, -110, -220, -275, -550, -1100.

• Is 1100 a whole number?

Yes 1100 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 1100. Help him in finding the mean of 1100.

Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1100 is 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 25 + 44 + 50 + 55 + 100 + 110 + 220 + 275 + 550 + 1100 = 2604.
Hence, the mean of factors of 1100 is 2604 ÷ 18 = 144.67.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1100? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.
Negative factors are -1, -2, -4, -5, -10, -11, -20, -22, -25, -44, -50, -55, -100, -110, -220, -275, -550, -1100.

Joey wants to write all the prime factors of 1100 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1100 are 2, 2, 5, 5, 11.
So in exponential form it can be written as 22 x 52 x 11.

Kevin has been asked to write 17 factor(s) of 1100. Can you predict the answer?

17 factor(s) of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550.

Sammy is puzzled while calculating the prime factors of 1100. Can you help him find them?

Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.
Prime factors of 1100 are 2, 2, 5, 5, 11

What is prime factorization of 1100?

Prime factorization of 1100 is 2 x 2 x 5 x 5 x 11 = 22 x 52 x 11.

Can you help Rubel to find out the product of the even factors of 1100?

Factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.
Even factors of 1100 are 2, 4, 10, 20, 22, 44, 50, 100, 110, 220, 550, 1100.
Hence, product of even factors of 1100 is; 2 x 4 x 10 x 20 x 22 x 44 x 50 x 100 x 110 x 220 x 550 x 1100 = 113379904000000000000.