1. Steps to find factors of 999 using Division Method

Example: Find factors of 999

  • Divide 999 by 1: 999 ÷ 1 : Remainder = 0
  • Divide 999 by 3: 999 ÷ 3 : Remainder = 0
  • Divide 999 by 9: 999 ÷ 9 : Remainder = 0
  • Divide 999 by 27: 999 ÷ 27 : Remainder = 0
  • Divide 999 by 37: 999 ÷ 37 : Remainder = 0
  • Divide 999 by 111: 999 ÷ 111 : Remainder = 0
  • Divide 999 by 333: 999 ÷ 333 : Remainder = 0
  • Divide 999 by 999: 999 ÷ 999 : Remainder = 0

Hence, Factors of 999 are 1, 3, 9, 27, 37, 111, 333, and 999

2. Steps to find factors of 999 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 999 using the division method, follow these steps:

  • Step 1. Start dividing 999 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 999, which is 3. Divide 999 by 3 to obtain the quotient (333).
    999 ÷ 3 = 333
  • Step 3. Repeat step 1 with the obtained quotient (333).
    333 ÷ 3 = 111
    111 ÷ 3 = 37
    37 ÷ 37 = 1

So, the prime factorization of 999 is, 999 = 3 x 3 x 3 x 37.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 999 as shown below:

So, the prime factorization of 999 is, 999 = 3 x 3 x 3 x 37.

3. Find factors of 999 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 999 would be the two numbers which, when multiplied, give 999 as the result.

The following table represents the calculation of factors of 999 in pairs:

Factor Pair Pair Factorization
1 and 999 1 x 999 = 999
3 and 333 3 x 333 = 999
9 and 111 9 x 111 = 999
27 and 37 27 x 37 = 999

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 999. They are called negative pair factors.

Hence, the negative pairs of 999 would be ( -1 , -999 ) , ( -3 , -333 ) , ( -9 , -111 ) and ( -27 , -37 ) .

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 999 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, 27, 37, 111, 333, 999 are exact divisors of 999.
  • Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999. Each factor divides 999 without leaving a remainder.

Frequently Asked Questions

  • Which is the smallest prime factor of 999?

    Smallest prime factor of 999 is 3.

  • Is 999 a perfect square?

    No 999 is not a perfect square.

  • What are five multiples of 999?

    First five multiples of 999 are 1998, 2997, 3996, 4995, 5994.

  • What is prime factorization of 999?

    Prime factorization of 999 is 3 x 3 x 3 x 37.

  • What are factors of 999?

    Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999.

  • How do you find factors of a negative number? ( eg. -999 )?

    Factors of -999 are -1, -3, -9, -27, -37, -111, -333, -999.

  • Is 999 a whole number?

    Yes 999 is a whole number.

  • Which is greatest factor of 999?

    The greatest factor of 999 is 333.

  • What are the prime factors of 999?

    The factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999.
    Prime factors of 999 are 3, 3, 3, 37.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 999. Can you help her?

Prime factors of 999 are 3, 3, 3, 37.
Hence, the product of prime factors of 111.

Can you help Rubel to find out the product of the even factors of 999?

Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999.
Even factors of 999 are 0.
Hence, product of even factors of 999 is; 0 = 0.

Joy wants to calculate mean of all the factors of 999. Help him in finding the mean of 999.

Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 999 is 1 + 3 + 9 + 27 + 37 + 111 + 333 + 999 = 1520.
Hence, the mean of factors of 999 is 1520 ÷ 8 = 190.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 999? Help her in writing all the factors.

Positive factors are 1, 3, 9, 27, 37, 111, 333, 999.
Negative factors are -1, -3, -9, -27, -37, -111, -333, -999.

How many factors are there for 999?

Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999.
So there are in total 8 factors.

Joey wants to write all the prime factors of 999 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 999 are 3, 3, 3, 37.
So in exponential form it can be written as 33 x 37.

Kevin has been asked to write 7 factor(s) of 999. Can you predict the answer?

7 factor(s) of 999 are 1, 3, 9, 27, 37, 111, 333.