1. Steps to find factors of 369 using Division Method

Example: Find factors of 369

  • Divide 369 by 1: 369 ÷ 1 : Remainder = 0
  • Divide 369 by 3: 369 ÷ 3 : Remainder = 0
  • Divide 369 by 9: 369 ÷ 9 : Remainder = 0
  • Divide 369 by 41: 369 ÷ 41 : Remainder = 0
  • Divide 369 by 123: 369 ÷ 123 : Remainder = 0
  • Divide 369 by 369: 369 ÷ 369 : Remainder = 0

Hence, Factors of 369 are 1, 3, 9, 41, 123, and 369

2. Steps to find factors of 369 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 369 using the division method, follow these steps:

  • Step 1. Start dividing 369 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 369, which is 3. Divide 369 by 3 to obtain the quotient (123).
    369 ÷ 3 = 123
  • Step 3. Repeat step 1 with the obtained quotient (123).
    123 ÷ 3 = 41
    41 ÷ 41 = 1

So, the prime factorization of 369 is, 369 = 3 x 3 x 41.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 369 as shown below:

So, the prime factorization of 369 is, 369 = 3 x 3 x 41.

3. Find factors of 369 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 369 would be the two numbers which, when multiplied, give 369 as the result.

The following table represents the calculation of factors of 369 in pairs:

Factor Pair Pair Factorization
1 and 369 1 x 369 = 369
3 and 123 3 x 123 = 369
9 and 41 9 x 41 = 369

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 369. They are called negative pair factors.

Hence, the negative pairs of 369 would be ( -1 , -369 ) , ( -3 , -123 ) and ( -9 , -41 ) .

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 factor of a number is an exact divisor of that number, example 1, 3, 9, 41, 123, 369 are exact divisors of 369.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 369 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 369.

Frequently Asked Questions

  • Which is the smallest prime factor of 369?

    Smallest prime factor of 369 is 3.

  • Is 369 a perfect square?

    No 369 is not a perfect square.

  • What are five multiples of 369?

    First five multiples of 369 are 738, 1107, 1476, 1845, 2214.

  • What is prime factorization of 369?

    Prime factorization of 369 is 3 x 3 x 41.

  • What are factors of 369?

    Factors of 369 are 1, 3, 9, 41, 123, 369.

  • How do you find factors of a negative number? ( eg. -369 )?

    Factors of -369 are -1, -3, -9, -41, -123, -369.

  • Is 369 a whole number?

    Yes 369 is a whole number.

  • Which is greatest factor of 369?

    The greatest factor of 369 is 123.

  • What are the prime factors of 369?

    The factors of 369 are 1, 3, 9, 41, 123, 369.
    Prime factors of 369 are 3, 3, 41.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 369. Can you help her?

Prime factors of 369 are 3, 3, 41.
Hence, the product of prime factors of 123.

Can you help Rubel to find out the product of the even factors of 369?

Factors of 369 are 1, 3, 9, 41, 123, 369.
Even factors of 369 are 0.
Hence, product of even factors of 369 is; 0 = 0.

Joy wants to calculate mean of all the factors of 369. Help him in finding the mean of 369.

Factors of 369 are 1, 3, 9, 41, 123, 369.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 369 is 1 + 3 + 9 + 41 + 123 + 369 = 546.
Hence, the mean of factors of 369 is 546 ÷ 6 = 91.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 369? Help her in writing all the factors.

Positive factors are 1, 3, 9, 41, 123, 369.
Negative factors are -1, -3, -9, -41, -123, -369.

How many factors are there for 369?

Factors of 369 are 1, 3, 9, 41, 123, 369.
So there are in total 6 factors.

Joey wants to write all the prime factors of 369 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 369 are 3, 3, 41.
So in exponential form it can be written as 32 x 41.

Kevin has been asked to write 5 factor(s) of 369. Can you predict the answer?

5 factor(s) of 369 are 1, 3, 9, 41, 123.