1. Steps to find factors of 459 using Division Method

Example: Find factors of 459

  • Divide 459 by 1: 459 ÷ 1 : Remainder = 0
  • Divide 459 by 3: 459 ÷ 3 : Remainder = 0
  • Divide 459 by 9: 459 ÷ 9 : Remainder = 0
  • Divide 459 by 17: 459 ÷ 17 : Remainder = 0
  • Divide 459 by 27: 459 ÷ 27 : Remainder = 0
  • Divide 459 by 51: 459 ÷ 51 : Remainder = 0
  • Divide 459 by 153: 459 ÷ 153 : Remainder = 0
  • Divide 459 by 459: 459 ÷ 459 : Remainder = 0

Hence, Factors of 459 are 1, 3, 9, 17, 27, 51, 153, and 459

2. Steps to find factors of 459 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 459 using the division method, follow these steps:

  • Step 1. Start dividing 459 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 459, which is 3. Divide 459 by 3 to obtain the quotient (153).
    459 ÷ 3 = 153
  • Step 3. Repeat step 1 with the obtained quotient (153).
    153 ÷ 3 = 51
    51 ÷ 3 = 17
    17 ÷ 17 = 1

So, the prime factorization of 459 is, 459 = 3 x 3 x 3 x 17.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 459 as shown below:

So, the prime factorization of 459 is, 459 = 3 x 3 x 3 x 17.

3. Find factors of 459 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 459 would be the two numbers which, when multiplied, give 459 as the result.

The following table represents the calculation of factors of 459 in pairs:

Factor Pair Pair Factorization
1 and 459 1 x 459 = 459
3 and 153 3 x 153 = 459
9 and 51 9 x 51 = 459
17 and 27 17 x 27 = 459

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 459. They are called negative pair factors.

Hence, the negative pairs of 459 would be ( -1 , -459 ) , ( -3 , -153 ) , ( -9 , -51 ) and ( -17 , -27 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Every number is a factor of zero (0), since 459 x 0 = 0.
  • 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, 3, 9, 17, 27, 51, 153, 459 are exact divisors of 459.
  • Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. Each factor divides 459 without leaving a remainder.

Frequently Asked Questions

  • Which is the smallest prime factor of 459?

    Smallest prime factor of 459 is 3.

  • Is 459 a perfect square?

    No 459 is not a perfect square.

  • What are five multiples of 459?

    First five multiples of 459 are 918, 1377, 1836, 2295, 2754.

  • What is prime factorization of 459?

    Prime factorization of 459 is 3 x 3 x 3 x 17.

  • What are factors of 459?

    Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459.

  • How do you find factors of a negative number? ( eg. -459 )?

    Factors of -459 are -1, -3, -9, -17, -27, -51, -153, -459.

  • Is 459 a whole number?

    Yes 459 is a whole number.

  • Which is greatest factor of 459?

    The greatest factor of 459 is 153.

  • What are the prime factors of 459?

    The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459.
    Prime factors of 459 are 3, 3, 3, 17.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 459. Can you help her?

Prime factors of 459 are 3, 3, 3, 17.
Hence, the product of prime factors of 51.

Can you help Rubel to find out the product of the even factors of 459?

Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459.
Even factors of 459 are 0.
Hence, product of even factors of 459 is; 0 = 0.

Joy wants to calculate mean of all the factors of 459. Help him in finding the mean of 459.

Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 459 is 1 + 3 + 9 + 17 + 27 + 51 + 153 + 459 = 720.
Hence, the mean of factors of 459 is 720 ÷ 8 = 90.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 459? Help her in writing all the factors.

Positive factors are 1, 3, 9, 17, 27, 51, 153, 459.
Negative factors are -1, -3, -9, -17, -27, -51, -153, -459.

How many factors are there for 459?

Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459.
So there are in total 8 factors.

Joey wants to write all the prime factors of 459 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 459 are 3, 3, 3, 17.
So in exponential form it can be written as 33 x 17.

Kevin has been asked to write 7 factor(s) of 459. Can you predict the answer?

7 factor(s) of 459 are 1, 3, 9, 17, 27, 51, 153.