Factors of 15 are the list of integers that can be evenly divided into 15. It has a total of 4 factors of which 15 is the biggest factor and the positive factors of 15 are 1, 3, 5, and 15. The sum of all factors of 15 is 24 and its factors in Pairs are (1, 15) and (3, 5).

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Factors of 15: 1, 3, 5 and 15Negative Factors of 15: -1, -3, -5 and -15Prime Factors of 15: 3, 5Prime Factorization of 15: 3 × 5 = 3 × 5Sum of Factors of 15: 24

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1.What Are the Factors of 15?
2.How to Calculate the Factors of 15?
3.Factors of 15 by Prime Factorization
4.Factors of 15 in Pairs
5.FAQs on Factors of 15

What Are the Factors of 15?


The factor of any number includes the pair of numbers that give the number as the result when they are multiplied with each other. In this case, 15 is a composite number because it can be divided by 1, 3, 5, and itself. Hence, 1, 3, 5 are the factors of 15. Also, all numbers are their own factors as well apart from number 1. Thus, 15 is also a factor of itself.


Important NotesAll the numbers have at least two factors. Among these two numbers, the first factor is 1 and the other is the number itself.


How to Calculate the Factors of 15?

To find all the factors of 15, we have to make all the possible pairs of numbers and multiply them to see if the result is 15 or not.

For example, 1 × 15 = 15 and 2 × 7.5 = 15, but since a factor cannot be a decimal number, 2 cannot be a factor of 15. 

Similarly, 3 × 5 = 15, and 15 × 1 = 15

That’s how you know that no other number apart from 1,3, 5, and 15 is a factor of 15.

Explore factors using illustrations and interactive examples


Factors of 15 by Prime Factorization

The factors of 15 are 1, 3, 5, and 15.

Let us understand this by performing prime factorization.

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Now that we have done the prime factorization of 15, we can multiply it and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.


Factors of 15 in Pairs

The pair factors can be any two numbers that, when multiplied with each other, gives the number as the product. In this case, the pair factors of 15 are:

3 × 5 = 15, hence, (3,5) is a pair factor.

1 × 15 = 15 is also a pair factor.

The positive pair factors of 15 are (1,15) and (3,5).

The negative pair factors of 15 are (-1,-15) and (-3,-5).


Tips and Tricks

Did you know that 1 is the smallest factor of all numbers?The given number is the largest factor of itself. For example, 6 is the largest factor of itself, 14 is the largest factor of itself, and so on.

Solved Examples


Example 1 Courtney has 5 friends. She has 15 chocolates. Can you explain how Courtney should divide the fifteen chocolates so that all her friends get an equal number of chocolates?

Solution

From the question, we know that she has 5 friends and 15 chocolates. Here, Courtney must use the concept of factors and multiples to divide the chocolates among her friends equally.

We know that 15 is a multiple of 5. We get the product 15 when we multiply 5 with 3.

Therefore, Courtney should distribute 3 chocolates each to her friends to divide the chocolates equally.


Example 2 A big square box can fit up to 15 equal-sized small wrist-watch boxes inside it. If 3 wrist-watch boxes can be kept in one row of the big box, how many rows will be required to keep all 15 boxes together in the big box?

Solution

Total number of wrist-watch boxes to be kept in the big box = 15

Total number of wrist-watch boxes in one row = 3

Now, if we simply divide 15 by 3, we get the answer 5, i.e. we need 5 rows of 3 wristwatches each to keep all the 15 wrist-watch boxes in the big box.

Here, we also learned that 3 and 5, are the factors of 15.

Therefore, 5 rows are required.


Example 3

Ashley is familiar with the concept of prime numbers. Hence, it will be easier for her to understand the factors of 15 through prime factorization. Can you help her with it?

Solution

Since Ashley is familiar with prime numbers, we will first list out all the prime numbers less than 15 and see how they divide 15.

Prime numbers less than 15 are 2, 3, 5, 7, 11, and 13.

Now, try to divide 15 with the above prime numbers.

15 ÷ 2 = 7.5, but we know that a factor cannot be a decimal number.

15 ÷ 3 = 5; we have 5 as the answer, thus, 5 is the factor of 15.

15 ÷ 5 = 3, here, 3 is also the factor of 15.

15 ÷ 7 = 2.14, is not a factor of 15 as it is a decimal.

Similarly, all the other prime numbers greater than five will give you the answer in a decimal number, which means that 5 is the highest prime factor of 15. Also, it is one of the only factors of 15 along with 1, 3, and 15 itself.


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FAQs on Factors of 15

What are the Factors of 15?

The factors of 15 are 1, 3, 5, 15 and its negative factors are -1, -3, -5, -15.

What is the Sum of the Factors of 15?

All the Factors of 15 are 1, 3, 5, 15 and therefore the sum of all these factors is 1 + 3 + 5 + 15 = 24

What Numbers are the Prime Factors of 15?

The prime factors of 15 are 3, 5.

What is the Greatest Common Factor of 15 and 10?

The factors of 15 and 10 are 1, 3, 5, 15 and 1, 2, 5, 10 respectively.Common factors of 15 and 10 are <1, 5>.Hence, the GCF of 15 and 10 is 5.

See more: Excel Gloss A Workbook Sheet That Contains Only A Chart, Excel Ch 3 Mos Terms (Stewart) Flashcards

What are the Common Factors of 15 and 9?

Since, the factors of 15 are 1, 3, 5, 15 and the factors of 9 are 1, 3, 9.Hence, <1, 3> are the common factors of 15 and 9.