1. Steps to find factors of 1365 using Division Method

Example: Find factors of 1365

  • Divide 1365 by 1: 1365 ÷ 1 : Remainder = 0
  • Divide 1365 by 3: 1365 ÷ 3 : Remainder = 0
  • Divide 1365 by 5: 1365 ÷ 5 : Remainder = 0
  • Divide 1365 by 7: 1365 ÷ 7 : Remainder = 0
  • Divide 1365 by 13: 1365 ÷ 13 : Remainder = 0
  • Divide 1365 by 15: 1365 ÷ 15 : Remainder = 0
  • Divide 1365 by 21: 1365 ÷ 21 : Remainder = 0
  • Divide 1365 by 35: 1365 ÷ 35 : Remainder = 0
  • Divide 1365 by 39: 1365 ÷ 39 : Remainder = 0
  • Divide 1365 by 65: 1365 ÷ 65 : Remainder = 0
  • Divide 1365 by 91: 1365 ÷ 91 : Remainder = 0
  • Divide 1365 by 105: 1365 ÷ 105 : Remainder = 0
  • Divide 1365 by 195: 1365 ÷ 195 : Remainder = 0
  • Divide 1365 by 273: 1365 ÷ 273 : Remainder = 0
  • Divide 1365 by 455: 1365 ÷ 455 : Remainder = 0
  • Divide 1365 by 1365: 1365 ÷ 1365 : Remainder = 0

Hence, Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, and 1365

2. Steps to find factors of 1365 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 1365 using the division method, follow these steps:

  • Step 1. Start dividing 1365 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 1365, which is 3. Divide 1365 by 3 to obtain the quotient (455).
    1365 ÷ 3 = 455
  • Step 3. Repeat step 1 with the obtained quotient (455).
    455 ÷ 5 = 91
    91 ÷ 7 = 13
    13 ÷ 13 = 1

So, the prime factorization of 1365 is, 1365 = 3 x 5 x 7 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1365 as shown below:

So, the prime factorization of 1365 is, 1365 = 3 x 5 x 7 x 13.

3. Find factors of 1365 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 1365 would be the two numbers which, when multiplied, give 1365 as the result.

The following table represents the calculation of factors of 1365 in pairs:

Factor Pair Pair Factorization
1 and 1365 1 x 1365 = 1365
3 and 455 3 x 455 = 1365
5 and 273 5 x 273 = 1365
7 and 195 7 x 195 = 1365
13 and 105 13 x 105 = 1365
15 and 91 15 x 91 = 1365
21 and 65 21 x 65 = 1365
35 and 39 35 x 39 = 1365

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 1365. They are called negative pair factors.

Hence, the negative pairs of 1365 would be ( -1 , -1365 ) , ( -3 , -455 ) , ( -5 , -273 ) , ( -7 , -195 ) , ( -13 , -105 ) , ( -15 , -91 ) , ( -21 , -65 ) and ( -35 , -39 ) .

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

  • Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365 are exact divisors of 1365.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 1365 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1365.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -1365 )?

    Factors of -1365 are -1, -3, -5, -7, -13, -15, -21, -35, -39, -65, -91, -105, -195, -273, -455, -1365.

  • What is the sum of all factors of 1365?

    The sum of all factors of 1365 is 2688.

  • What is prime factorization of 1365?

    Prime factorization of 1365 is 3 x 5 x 7 x 13.

  • What are the pair factors of 1365?

    Pair factors of 1365 are (1,1365), (3,455), (5,273), (7,195), (13,105), (15,91), (21,65), (35,39).

  • What are six multiples of 1365?

    First five multiples of 1365 are 2730, 4095, 5460, 6825, 8190, 9555.

  • Is 1365 a whole number?

    Yes 1365 is a whole number.

  • Which is the smallest prime factor of 1365?

    Smallest prime factor of 1365 is 3.

  • What are five multiples of 1365?

    First five multiples of 1365 are 2730, 4095, 5460, 6825, 8190.

  • Write all factors of 1365?

    Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.

Examples of Factors

Joey wants to write all the prime factors of 1365 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1365 are 3, 5, 7, 13.
So in exponential form it can be written as 3 x 5 x 7 x 13.

How many factors are there for 1365?

Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 1365. Can you predict the answer?

15 factor(s) of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455.

Sammy is puzzled while calculating the prime factors of 1365. Can you help him find them?

Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.
Prime factors of 1365 are 3, 5, 7, 13

What is prime factorization of 1365?

Prime factorization of 1365 is 3 x 5 x 7 x 13 = 3 x 5 x 7 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 1365. Can you help her?

Prime factors of 1365 are 3, 5, 7, 13.
Hence, the product of prime factors of 1365.

Can you help Rubel to find out the product of the even factors of 1365?

Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.
Even factors of 1365 are 0.
Hence, product of even factors of 1365 is; 0 = 0.