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Factors of 920

Factors of 920 are numbers that, when multiplied in pairs give the product as 920. It has total 16 factors of which 920 is the biggest factor and the prime factors of 920 are 2, 5, 23. The sum of all factors of 920 is 2160.

All Factors of 920: 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460 and 920
Prime Factors of 920: 2, 5, 23
Prime Factorization of 920: 2³ × 5¹ × 23¹
Sum of Factors of 920: 2160

1.	What Are the Factors of 920?
2.	Factors of 920 by Prime Factorization
3.	Factors of 920 in Pairs
4.	FAQs on Factors of 920

What are Factors of 920?

Factors of 920 are pairs of those numbers whose products result in 920. These factors are either prime numbers or composite numbers.

How to Find the Factors of 920?

To find the factors of 920, we will have to find the list of numbers that would divide 920 without leaving any remainder.

920/5 = 184; therefore, 5 is a factor of 920 and 184 is also a factor of 920.
920/23 = 40; therefore, 23 is a factor of 920 and 40 is also a factor of 920.

Similarly we can find other factors. Hence, the factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920.

☛ Also Check:

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
Factors of 19 - The factors of 19 are 1, 19
Factors of 31 - The factors of 31 are 1, 31
Factors of 14 - The factors of 14 are 1, 2, 7, 14
Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

Factors of 920 by Prime Factorization

The number 920 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 920. The first step is to divide the number 920 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

920 ÷ 2 = 460
460 ÷ 2 = 230
230 ÷ 2 = 115

Further dividing 115 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 115 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 920 can be written as 2³ × 5¹ × 23¹ where 2, 5, 23 are prime.

Factors of 920 in Pairs

Pair factors of 920 are the pairs of numbers that when multiplied give the product 920. The factors of 920 in pairs are:

1 × 920 = (1, 920)
2 × 460 = (2, 460)
4 × 230 = (4, 230)
5 × 184 = (5, 184)
8 × 115 = (8, 115)
10 × 92 = (10, 92)
20 × 46 = (20, 46)
23 × 40 = (23, 40)

Negative pair factors of 920 are:

-1 × -920 = (-1, -920)
-2 × -460 = (-2, -460)
-4 × -230 = (-4, -230)
-5 × -184 = (-5, -184)
-8 × -115 = (-8, -115)
-10 × -92 = (-10, -92)
-20 × -46 = (-20, -46)
-23 × -40 = (-23, -40)

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

Factors of 920 Solved Examples

Example 1: How many factors are there for 920?

Solution:

The factors of 920 are too many, therefore if we can find the prime factorization of 920, 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 920 = 2³ × 5¹ × 23¹
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 920 and 476.

Solution:

The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920 and factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.

Therefore, the Least Common Multiple of 920 and 476 is 109480 and Greatest Common Divisor (GCD) of 920 and 476 is 4.
Example 3: Find if 2, 4, 20, 23, 40, 46, 217 and 920 are factors of 920.

Solution:

When we divide 920 by 217 it leaves a remainder. Therefore, the number 217 is not a factor of 920. All numbers except 217 are factors of 920.
Example 4: Find the product of all the prime factors of 920.

Solution:

Since, the prime factors of 920 are 2, 5, 23. Therefore, the product of prime factors = 2 × 5 × 23 = 230.

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Q. 1

Choose True or False for the following statement.

Every number is the greatest factor of itself.
Q. 2

If 3 is a factor of 21, then 21 divided by 3 leaves as the remainder.

FAQs on Factors of 920

What are the Factors of 920?

The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920 and its negative factors are -1, -2, -4, -5, -8, -10, -20, -23, -40, -46, -92, -115, -184, -230, -460, -920.

What is the Sum of Factors of 920?

Sum of all factors of 920 = (2^{3 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 2160

What are the Prime Factors of 920?

The prime factors of 920 are 2, 5, 23.

What is the Greatest Common Factor of 920 and 902?

The factors of 920 and 902 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920 and 1, 2, 11, 22, 41, 82, 451, 902 respectively.

Common factors of 920 and 902 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 920 and 902 is 2.

How Many Factors of 787 are also common to the Factors of 920?

Since, the factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920 and factors of 787 are 1, 787. Hence, 920 and 787 have only one common factor which is 1. Therefore, 920 and 787 are co-prime.

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