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Factors of 810

Factors of 810 are the list of integers that can be evenly divided into 810. There are 20 factors of 810 of which 810 itself is the biggest factor and its prime factors are 2, 3, 5 The sum of all factors of 810 is 2178.

All Factors of 810: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 and 810
Prime Factors of 810: 2, 3, 5
Prime Factorization of 810: 2¹ × 3⁴ × 5¹
Sum of Factors of 810: 2178

1.	What Are the Factors of 810?
2.	Factors of 810 by Prime Factorization
3.	Factors of 810 in Pairs
4.	FAQs on Factors of 810

What are Factors of 810?

Factors of 810 are pairs of those numbers whose products result in 810. These factors are either prime numbers or composite numbers.

How to Find the Factors of 810?

To find the factors of 810, we will have to find the list of numbers that would divide 810 without leaving any remainder.

810/10 = 81; therefore, 10 is a factor of 810 and 81 is also a factor of 810.
810/45 = 18; therefore, 45 is a factor of 810 and 18 is also a factor of 810.

Similarly we can find other factors. Hence, the factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.

☛ Also Check:

Factors of 29 - The factors of 29 are 1, 29
Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 57 - The factors of 57 are 1, 3, 19, 57
Factors of 21 - The factors of 21 are 1, 3, 7, 21
Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 810 by Prime Factorization

The number 810 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 810. The first step is to divide the number 810 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

810 ÷ 2 = 405

Further dividing 405 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 405 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 810 can be written as 2¹ × 3⁴ × 5¹ where 2, 3, 5 are prime.

Factors of 810 in Pairs

Pair factors of 810 are the pairs of numbers that when multiplied give the product 810. The factors of 810 in pairs are:

1 × 810 = (1, 810)
2 × 405 = (2, 405)
3 × 270 = (3, 270)
5 × 162 = (5, 162)
6 × 135 = (6, 135)
9 × 90 = (9, 90)
10 × 81 = (10, 81)
15 × 54 = (15, 54)
18 × 45 = (18, 45)
27 × 30 = (27, 30)

Negative pair factors of 810 are:

-1 × -810 = (-1, -810)
-2 × -405 = (-2, -405)
-3 × -270 = (-3, -270)
-5 × -162 = (-5, -162)
-6 × -135 = (-6, -135)
-9 × -90 = (-9, -90)
-10 × -81 = (-10, -81)
-15 × -54 = (-15, -54)
-18 × -45 = (-18, -45)
-27 × -30 = (-27, -30)

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

Factors of 810 Solved Examples

Example 1: How many factors are there for 810?

Solution:

The factors of 810 are too many, therefore if we can find the prime factorization of 810, 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 810 = 2¹ × 3⁴ × 5¹
Therefore, the total number of factors are (1 + 1) × (4 + 1) × (1 + 1) = 2 × 5 × 2 = 20
Example 2: Find the LCM and Greatest Common Factor (GCF) of 810 and 292.

Solution:

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810 and factors of 292 are 1, 2, 4, 73, 146, 292.

Therefore, the LCM of 810 and 292 is 118260 and Greatest Common Factor (GCF) of 810 and 292 is 2.
Example 3: Find if 2, 9, 10, 45, 177, 270, 405 and 810 are factors of 810.

Solution:

When we divide 810 by 177 it leaves a remainder. Therefore, the number 177 is not a factor of 810. All numbers except 177 are factors of 810.
Example 4: Find the product of all the prime factors of 810.

Solution:

Since, the prime factors of 810 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 810

What are the Factors of 810?

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810 and its negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -270, -405, -810.

What is the Sum of all Factors of 810?

Sum of all factors of 810 = (2^{1 + 1} - 1)/(2 - 1) × (3^{4 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) = 2178

What are the Prime Factors of 810?

The prime factors of 810 are 2, 3, 5.

What is the Greatest Common Factor of 810 and 721?

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810 and the factors of 721 are 1, 7, 103, 721. 810 and 721 have only one common factor which is 1. This implies that 810 and 721 are co-prime.

Hence, the Greatest Common Factor (GCF) of 810 and 721 is 1.

How Many Factors of 810 are also Factors of 43?

Since, the factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810 and factors of 43 are 1, 43. Hence, 810 and 43 have only one common factor which is 1. Therefore, 810 and 43 are co-prime.

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