Factors of 360

2. Steps to find factors of 360 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 360 using the division method, follow these steps:

• Step 1. Start dividing 360 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 360, which is 2. Divide 360 by 2 to obtain the quotient (180).
  360 ÷ 2 = 180
• Step 3. Repeat step 1 with the obtained quotient (180).
  180 ÷ 2 = 90
  90 ÷ 2 = 45
  45 ÷ 3 = 15
  15 ÷ 3 = 5
  5 ÷ 5 = 1

So, the prime factorization of 360 is, 360 = 2 x 2 x 2 x 3 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 360 as shown below:

So, the prime factorization of 360 is, 360 = 2 x 2 x 2 x 3 x 3 x 5.

3. Find factors of 360 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 360 would be the two numbers which, when multiplied, give 360 as the result.

The following table represents the calculation of factors of 360 in pairs:

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 360. They are called negative pair factors.

Hence, the negative pairs of 360 would be ( -1 , -360 ) , ( -2 , -180 ) , ( -3 , -120 ) , ( -4 , -90 ) , ( -5 , -72 ) , ( -6 , -60 ) , ( -8 , -45 ) , ( -9 , -40 ) , ( -10 , -36 ) , ( -12 , -30 ) , ( -15 , -24 ) and ( -18 , -20 ) .

What are factors?

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

Properties of factors

• Each number is a factor of itself. Eg. 360 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 360.
• Every number is a factor of zero (0), since 360 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, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 are exact divisors of 360.
• Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Each factor divides 360 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 are all less than or equal to 360.

Frequently Asked Questions

• Which is the smallest prime factor of 360?

  Smallest prime factor of 360 is 2.

• Is 360 a perfect square?

  No 360 is not a perfect square.

• What are five multiples of 360?

  First five multiples of 360 are 720, 1080, 1440, 1800, 2160.

• What is prime factorization of 360?

  Prime factorization of 360 is 2 x 2 x 2 x 3 x 3 x 5.

• What are factors of 360?

  Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

• How do you find factors of a negative number? ( eg. -360 )?

  Factors of -360 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -30, -36, -40, -45, -60, -72, -90, -120, -180, -360.

• Is 360 a whole number?

  Yes 360 is a whole number.

• Which is greatest factor of 360?

  The greatest factor of 360 is 180.

• What are the prime factors of 360?

  The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
  Prime factors of 360 are 2, 2, 2, 3, 3, 5.

Examples of Factors