A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

 

Factors of 1365

Factors of 1365 are numbers that, when multiplied in pairs give the product as 1365. There are 16 factors of 1365, of which the following are its prime factors 3, 5, 7, 13. The sum of all factors of 1365 is 2688.

  • All Factors of 1365: 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455 and 1365
  • Prime Factors of 1365: 3, 5, 7, 13
  • Prime Factorization of 1365: 31 × 51 × 71 × 131
  • Sum of Factors of 1365: 2688
1. What Are the Factors of 1365?
2. Factors of 1365 by Prime Factorization
3. Factors of 1365 in Pairs
4. FAQs on Factors of 1365
Factors of 1365

What are Factors of 1365?

Factors of 1365 are pairs of those numbers whose products result in 1365. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1365?

To find the factors of 1365, we will have to find the list of numbers that would divide 1365 without leaving any remainder.

  • 1365/1 = 1365; therefore, 1 is a factor of 1365.
  • 1365/13 = 105; therefore, 13 is a factor of 1365.
Similarly we can find other factors. Hence, the factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.

☛ Also Check:

Factors of 1365 by Prime Factorization

The number 1365 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1365. The first step is to divide the number 1365 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1365 ÷ 3 = 455

Further dividing 455 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 455 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1365 can be written as 31 × 51 × 71 × 131 where 3, 5, 7, 13 are prime.

 

Factors of 1365 in Pairs

Pair factors of 1365 are the pairs of numbers that when multiplied give the product 1365. The factors of 1365 in pairs are:

  • 1 × 1365 = (1, 1365)
  • 3 × 455 = (3, 455)
  • 5 × 273 = (5, 273)
  • 7 × 195 = (7, 195)
  • 13 × 105 = (13, 105)
  • 15 × 91 = (15, 91)
  • 21 × 65 = (21, 65)
  • 35 × 39 = (35, 39)

Negative pair factors of 1365 are:

  • -1 × -1365 = (-1, -1365)
  • -3 × -455 = (-3, -455)
  • -5 × -273 = (-5, -273)
  • -7 × -195 = (-7, -195)
  • -13 × -105 = (-13, -105)
  • -15 × -91 = (-15, -91)
  • -21 × -65 = (-21, -65)
  • -35 × -39 = (-35, -39)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1365 Solved Examples

  1. Example 1: How many factors are there for 1365?

    Solution:

    The factors of 1365 are too many, therefore if we can find the prime factorization of 1365, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 1365 = 31 × 51 × 71 × 131
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1365 and 893.

    Solution:

    The factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365 and factors of 893 are 1, 19, 47, 893.

    Therefore, the Least Common Multiple of 1365 and 893 is 1218945 and Greatest Common Divisor (GCD) of 1365 and 893 is 1.

  3. Example 3: Find if 3, 5, 15, 21, 35, 65, 195 and 1261 are factors of 1365.

    Solution:

    When we divide 1365 by 1261 it leaves a remainder. Therefore, the number 1261 is not a factor of 1365. All numbers except 1261 are factors of 1365.

  4. Example 4: Find the product of all the prime factors of 1365.

    Solution:

    Since, the prime factors of 1365 are 3, 5, 7, 13. Therefore, the product of prime factors = 3 × 5 × 7 × 13 = 1365.

Show Solution >

go to slidego to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

 

FAQs on Factors of 1365

What are the Factors of 1365?

The factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365 and its negative factors 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?

Sum of all factors of 1365 = (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (131 + 1 - 1)/(13 - 1) = 2688

What are Pair Factors of 1365?

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

What is the Greatest Common Factor of 1365 and 1149?

The factors of 1365 and 1149 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365 and 1, 3, 383, 1149 respectively.

Common factors of 1365 and 1149 are [1, 3].

Hence, the GCF of 1365 and 1149 is 3.

How Many Factors of 858 are also common to the Factors of 1365?

Since, the factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365 and the factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858.
Hence, [1, 3, 13, 39] are the common factors of 1365 and 858.

Math worksheets and
visual curriculum