Factors of 1100

Factors of 1100 are the list of integers that we can split evenly into 1100. There are overall 18 factors of 1100 among which 1100 is the biggest factor and its prime factors are 2, 5, 11. The sum of all factors of 1100 is 2604.

All Factors of 1100: 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550 and 1100
Prime Factors of 1100: 2, 5, 11
Prime Factorization of 1100: 2² × 5² × 11¹
Sum of Factors of 1100: 2604

1.	What Are the Factors of 1100?
2.	Factors of 1100 by Prime Factorization
3.	Factors of 1100 in Pairs
4.	FAQs on Factors of 1100

What are Factors of 1100?

Factors of 1100 are pairs of those numbers whose products result in 1100. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1100?

To find the factors of 1100, we will have to find the list of numbers that would divide 1100 without leaving any remainder.

1100/50 = 22; therefore, 50 is a factor of 1100 and 22 is also a factor of 1100.
1100/100 = 11; therefore, 100 is a factor of 1100 and 11 is also a factor of 1100.

Similarly we can find other factors. Hence, the factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.

☛ Also Check:

Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 22 - The factors of 22 are 1, 2, 11, 22
Factors of 5 - The factors of 5 are 1, 5
Factors of 19 - The factors of 19 are 1, 19

Factors of 1100 by Prime Factorization

The number 1100 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1100. The first step is to divide the number 1100 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1100 ÷ 2 = 550
550 ÷ 2 = 275

Further dividing 275 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 275 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1100 can be written as 2² × 5² × 11¹ where 2, 5, 11 are prime.

Factors of 1100 in Pairs

Pair factors of 1100 are the pairs of numbers that when multiplied give the product 1100. The factors of 1100 in pairs are:

1 × 1100 = (1, 1100)
2 × 550 = (2, 550)
4 × 275 = (4, 275)
5 × 220 = (5, 220)
10 × 110 = (10, 110)
11 × 100 = (11, 100)
20 × 55 = (20, 55)
22 × 50 = (22, 50)
25 × 44 = (25, 44)

Negative pair factors of 1100 are:

-1 × -1100 = (-1, -1100)
-2 × -550 = (-2, -550)
-4 × -275 = (-4, -275)
-5 × -220 = (-5, -220)
-10 × -110 = (-10, -110)
-11 × -100 = (-11, -100)
-20 × -55 = (-20, -55)
-22 × -50 = (-22, -50)
-25 × -44 = (-25, -44)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1100 Solved Examples

Example 1: How many factors are there for 1100?

Solution:

The factors of 1100 are too many, therefore if we can find the prime factorization of 1100, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 1100 = 2² × 5² × 11¹
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1100 and 121.

Solution:

The factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 and factors of 121 are 1, 11, 121.

Therefore, the Lowest Common Multiple (LCM) of 1100 and 121 is 12100 and Greatest Common Divisor (GCD) of 1100 and 121 is 11.
Example 3: Find if 11, 22, 50, 110, 275, 550, 746 and 1100 are factors of 1100.

Solution:

When we divide 1100 by 746 it leaves a remainder. Therefore, the number 746 is not a factor of 1100. All numbers except 746 are factors of 1100.
Example 4: Find the product of all the prime factors of 1100.

Solution:

Since, the prime factors of 1100 are 2, 5, 11. Therefore, the product of prime factors = 2 × 5 × 11 = 110.

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FAQs on Factors of 1100

What are the Factors of 1100?

The factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 and its negative factors are -1, -2, -4, -5, -10, -11, -20, -22, -25, -44, -50, -55, -100, -110, -220, -275, -550, -1100.

What is the Sum of all the Factors of 1100?

Sum of all factors of 1100 = (2^{2 + 1} - 1)/(2 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 2604

What are the Prime Factors of 1100?

The prime factors of 1100 are 2, 5, 11.

What is the Greatest Common Factor of 1100 and 260?

The factors of 1100 and 260 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 and 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260 respectively.

Common factors of 1100 and 260 are [1, 2, 4, 5, 10, 20].

Hence, the Greatest Common Factor of 1100 and 260 is 20.

How Many Factors of 837 are also common to the Factors of 1100?

Since, the factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 and factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837. Hence, 1100 and 837 have only one common factor which is 1. Therefore, 1100 and 837 are co-prime.

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