1. Steps to find factors of 518 using Division Method

Example: Find factors of 518

  • Divide 518 by 1: 518 ÷ 1 : Remainder = 0
  • Divide 518 by 2: 518 ÷ 2 : Remainder = 0
  • Divide 518 by 7: 518 ÷ 7 : Remainder = 0
  • Divide 518 by 14: 518 ÷ 14 : Remainder = 0
  • Divide 518 by 37: 518 ÷ 37 : Remainder = 0
  • Divide 518 by 74: 518 ÷ 74 : Remainder = 0
  • Divide 518 by 259: 518 ÷ 259 : Remainder = 0
  • Divide 518 by 518: 518 ÷ 518 : Remainder = 0

Hence, Factors of 518 are 1, 2, 7, 14, 37, 74, 259, and 518

2. Steps to find factors of 518 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 518 using the division method, follow these steps:

  • Step 1. Start dividing 518 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 518, which is 2. Divide 518 by 2 to obtain the quotient (259).
    518 ÷ 2 = 259
  • Step 3. Repeat step 1 with the obtained quotient (259).
    259 ÷ 7 = 37
    37 ÷ 37 = 1

So, the prime factorization of 518 is, 518 = 2 x 7 x 37.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 518 as shown below:

So, the prime factorization of 518 is, 518 = 2 x 7 x 37.

3. Find factors of 518 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 518 would be the two numbers which, when multiplied, give 518 as the result.

The following table represents the calculation of factors of 518 in pairs:

Factor Pair Pair Factorization
1 and 518 1 x 518 = 518
2 and 259 2 x 259 = 518
7 and 74 7 x 74 = 518
14 and 37 14 x 37 = 518

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 518. They are called negative pair factors.

Hence, the negative pairs of 518 would be ( -1 , -518 ) , ( -2 , -259 ) , ( -7 , -74 ) and ( -14 , -37 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 518 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 7, 14, 37, 74, 259, 518 are exact divisors of 518.
  • 1 is a factor of every number. Eg. 1 is a factor of 518.
  • Every number is a factor of zero (0), since 518 x 0 = 0.

Frequently Asked Questions

  • What are the pair factors of 518?

    Pair factors of 518 are (1,518), (2,259), (7,74), (14,37).

  • What are five multiples of 518?

    First five multiples of 518 are 1036, 1554, 2072, 2590, 3108.

  • What two numbers make 518?

    Two numbers that make 518 are 2 and 259.

  • What is the sum of all factors of 518?

    The sum of all factors of 518 is 912.

  • What are factors of -518?

    Factors of -518 are -1, -2, -7, -14, -37, -74, -259, -518.

  • What are factors of 518?

    Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518.

  • Is 518 a perfect square?

    No 518 is not a perfect square.

  • Which is the smallest prime factor of 518?

    Smallest prime factor of 518 is 2.

  • Which is greatest factor of 518?

    The greatest factor of 518 is 259.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 518?

Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518.
Odd factors of 518 are 1, 7, 37, 259.
Hence product of odd factors of 518 is; 1 x 7 x 37 x 259 = 67081.

Joey wants to write all the prime factors of 518 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 518 are 2, 7, 37.
So in exponential form it can be written as 2 x 7 x 37.

How many factors are there for 518?

Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 518. Can you predict the answer?

7 factor(s) of 518 are 1, 2, 7, 14, 37, 74, 259.

Sammy is puzzled while calculating the prime factors of 518. Can you help him find them?

Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518.
Prime factors of 518 are 2, 7, 37

What is prime factorization of 518?

Prime factorization of 518 is 2 x 7 x 37 = 2 x 7 x 37.

Can you help Rubel to find out the product of the even factors of 518?

Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518.
Even factors of 518 are 2, 14, 74, 518.
Hence, product of even factors of 518 is; 2 x 14 x 74 x 518 = 1073296.