Factors of 810

In this article, we will take the example of the factors of the number 810 and learn more about it. By applying the long division method on the number 810 we get to know that its factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 54, 45, 81, 135, 90, 162, 270, 405, and 810.

Negative factors of 810: Negative numbers that multiply a couple of times to produce -810, like -1, -2, -3, etc. paired with negative factors.

Prime factors of 810: Those prime numbers that when multiplied together in just the right amounts do equal 810. For 810 they are 1, 2, 3, and 5.

Prime factorization of 810: Expressing 810 as a product of primes: 810=2×3⁴×5.

Sum of factors of 810: Sum of all positive divisors of 810 is 2176. 
 

There are many simple methods which can be used by students to calculate factors of numbers. Below you can find some methods.

• Multiplication method

• Division method

• Prime factors and prime factorization

• Factor tree
   

In the multiplication method, we find the pairs of numbers, which when multiplied together provide the original number. For 810 the pairs are.

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

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

The division method states that any number that can divide the said number is considered as factors of the said number. Hence, any number that divides 810 evenly without leaving any reminder is considered as a factor of 810.

810÷1=810 (1 and 810 are factors)

810÷2=405 (2 and 405 are factors)

810÷3=270 (3 and 270 are factors)

810÷5=162 (5 and 162 are factors)

810÷6=135 (6 and 135 are factors)

810÷9=90 (9 and 90 are factors)

810÷10=81 (10 and 81 are factors)

810÷15=54 (15 and 54 are factors)

810÷18=45 (18 and 45 are factors)

810÷27=30 (27 and 30 are factors)
 

The prime factorization method is a simple method wherein the two prime numbers are multiplied together to derive the said number, these prime numbers are then considered as the factors.

Divide by 2 (smallest prime):

810÷2=405

Divide by 3:

405÷3=135, 135÷3=45, 45÷3=15, 15÷3=5

Divide by 5 (next prime):

5÷5=1

Hence, prime factorization of 810 is 2×3⁴×5

Factor tree is a mathematical diagram which repeatedly breaks down or divides the number by prime numbers until it reaches 0, or it cannot be further divided These numbers are then considered as the factors

• Divisor: The number that divides another number completely without remainder, it is called divisor. For example, 6 is divisible by 3, so the divisor is 3. 

• Multiple: A number multiplied by an integer. Is always greater or equal to the original number

• Prime Factor: It is a natural number whose only factor other than 1 will be itself.