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Factors of 440

Factors of 440 are integers that can be divided evenly into 440. There are 16 factors of 440 of which 440 itself is the biggest factor and its prime factors are 2, 5, 11 The sum of all factors of 440 is 1080.

All Factors of 440: 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220 and 440
Prime Factors of 440: 2, 5, 11
Prime Factorization of 440: 2³ × 5¹ × 11¹
Sum of Factors of 440: 1080

1.	What Are the Factors of 440?
2.	Factors of 440 by Prime Factorization
3.	Factors of 440 in Pairs
4.	FAQs on Factors of 440

What are Factors of 440?

Factors of 440 are pairs of those numbers whose products result in 440. These factors are either prime numbers or composite numbers.

How to Find the Factors of 440?

To find the factors of 440, we will have to find the list of numbers that would divide 440 without leaving any remainder.

440/220 = 2; therefore, 220 is a factor of 440 and 2 is also a factor of 440.
440/5 = 88; therefore, 5 is a factor of 440 and 88 is also a factor of 440.

Similarly we can find other factors. Hence, the factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440.

☛ Also Check:

Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 29 - The factors of 29 are 1, 29
Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
Factors of 13 - The factors of 13 are 1, 13
Factors of 35 - The factors of 35 are 1, 5, 7, 35

Factors of 440 by Prime Factorization

The number 440 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 440. The first step is to divide the number 440 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

440 ÷ 2 = 220
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 440 can be written as 2³ × 5¹ × 11¹ where 2, 5, 11 are prime.

Factors of 440 in Pairs

Pair factors of 440 are the pairs of numbers that when multiplied give the product 440. The factors of 440 in pairs are:

1 × 440 = (1, 440)
2 × 220 = (2, 220)
4 × 110 = (4, 110)
5 × 88 = (5, 88)
8 × 55 = (8, 55)
10 × 44 = (10, 44)
11 × 40 = (11, 40)
20 × 22 = (20, 22)

Negative pair factors of 440 are:

-1 × -440 = (-1, -440)
-2 × -220 = (-2, -220)
-4 × -110 = (-4, -110)
-5 × -88 = (-5, -88)
-8 × -55 = (-8, -55)
-10 × -44 = (-10, -44)
-11 × -40 = (-11, -40)
-20 × -22 = (-20, -22)

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

Factors of 440 Solved Examples

Example 1: How many factors are there for 440?

Solution:

The factors of 440 are too many, therefore if we can find the prime factorization of 440, 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 440 = 2³ × 5¹ × 11¹
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 440 and 199.

Solution:

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440 and factors of 199 are 1, 199.

Therefore, the Least Common Multiple of 440 and 199 is 87560 and Greatest Common Divisor (GCD) of 440 and 199 is 1.
Example 3: Find if 1, 10, 40, 44, 88, 97, 110 and 220 are factors of 440.

Solution:

When we divide 440 by 97 it leaves a remainder. Therefore, the number 97 is not a factor of 440. All numbers except 97 are factors of 440.
Example 4: Find the product of all the prime factors of 440.

Solution:

Since, the prime factors of 440 are 2, 5, 11. Therefore, the product of prime factors = 2 × 5 × 11 = 110.

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FAQs on Factors of 440

What are the Factors of 440?

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440 and its negative factors are -1, -2, -4, -5, -8, -10, -11, -20, -22, -40, -44, -55, -88, -110, -220, -440.

What is the Sum of the Factors of 440?

Sum of all factors of 440 = (2^{3 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 1080

What Numbers are the Prime Factors of 440?

The prime factors of 440 are 2, 5, 11.

What is the Greatest Common Factor of 440 and 241?

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440 and the factors of 241 are 1, 241. 440 and 241 have only one common factor which is 1. This implies that 440 and 241 are co-prime.

Hence, the Greatest Common Factor (GCF) of 440 and 241 is 1.

How Many Factors of 440 are also common to the Factors of 347?

Since, the factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440 and factors of 347 are 1, 347. Hence, 440 and 347 have only one common factor which is 1. Therefore, 440 and 347 are co-prime.

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