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Factors of 220

Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. The Prime Factorization of 220 is 2² × 5¹ × 11¹.

All Factors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and 220
Prime Factors of 220: 2, 5, 11
Prime Factorization of 220: 2² × 5¹ × 11¹
Sum of Factors of 220: 504

1.	What Are the Factors of 220?
2.	Factors of 220 by Prime Factorization
3.	Factors of 220 in Pairs
4.	FAQs on Factors of 220

What are Factors of 220?

Factors of 220 are pairs of those numbers whose products result in 220. These factors are either prime numbers or composite numbers.

How to Find the Factors of 220?

To find the factors of 220, we will have to find the list of numbers that would divide 220 without leaving any remainder.

220/220 = 1; therefore, 220 is a factor of 220.
220/44 = 5; therefore, 44 is a factor of 220.

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

☛ Also Check:

Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 27 - The factors of 27 are 1, 3, 9, 27

Factors of 220 by Prime Factorization

The number 220 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 220. The first step is to divide the number 220 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

220 ÷ 2 = 110
110 ÷ 2 = 55

Further dividing 55 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 55 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 220 can be written as 2² × 5¹ × 11¹ where 2, 5, 11 are prime.

Factors of 220 in Pairs

Pair factors of 220 are the pairs of numbers that when multiplied give the product 220. The factors of 220 in pairs are:

1 × 220 = (1, 220)
2 × 110 = (2, 110)
4 × 55 = (4, 55)
5 × 44 = (5, 44)
10 × 22 = (10, 22)
11 × 20 = (11, 20)

Negative pair factors of 220 are:

-1 × -220 = (-1, -220)
-2 × -110 = (-2, -110)
-4 × -55 = (-4, -55)
-5 × -44 = (-5, -44)
-10 × -22 = (-10, -22)
-11 × -20 = (-11, -20)

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

Factors of 220 Solved Examples

Example 1: How many factors are there for 220?

Solution:

The factors of 220 are too many, therefore if we can find the prime factorization of 220, 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 220 = 2² × 5¹ × 11¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 220 and 79.

Solution:

The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 and factors of 79 are 1, 79.

Therefore, the Least Common Multiple (LCM) of 220 and 79 is 17380 and Greatest Common Divisor (GCD) of 220 and 79 is 1.
Example 3: Find if 2, 4, 5, 11, 60, 110 and 220 are factors of 220.

Solution:

When we divide 220 by 60 it leaves a remainder. Therefore, the number 60 is not a factor of 220. All numbers except 60 are factors of 220.
Example 4: Find the product of all the prime factors of 220.

Solution:

Since, the prime factors of 220 are 2, 5, 11. Therefore, the product of prime factors = 2 × 5 × 11 = 110.

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FAQs on Factors of 220

What are the Factors of 220?

The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 and its negative factors are -1, -2, -4, -5, -10, -11, -20, -22, -44, -55, -110, -220.

What is the Sum of all Factors of 220?

Sum of all factors of 220 = (2^{2 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 504

What numbers are the Pair Factors of 220?

The pair factors of 220 are (1, 220), (2, 110), (4, 55), (5, 44), (10, 22), (11, 20).

What is the Greatest Common Factor of 220 and 136?

The factors of 220 and 136 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 and 1, 2, 4, 8, 17, 34, 68, 136 respectively.

Common factors of 220 and 136 are [1, 2, 4].

Hence, the Greatest Common Factor of 220 and 136 is 4.

How Many Factors of 220 are also common to the Factors of 109?

Since, the factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 and factors of 109 are 1, 109. Hence, 220 and 109 have only one common factor which is 1. Therefore, 220 and 109 are co-prime.

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