When we say that a number X is a factor of Y, then it means that the number X will be the result when 2 same numbers Y and Y’ are multiplied. Similarly, the factors of 15 are the integers that when multiplied to each other gives 15 itself as the result. Here, when the numbers are divided by 15, it will leave no reminder. Hence, they are said to be factors. This is quite an easy topic to learn and so, let’s study a few basic and important concepts about the factors of 15.

A Brief Account of What are the Factors of 15

When you multiply 2 whole numbers, the result is a product. Here, the 2 numbers put together during multiplication are termed as the factors. For example, if 5 × 3 gives 15, then you can say that 3 and 5 are the original factors for the number 15. Hence, 5 and 3 are termed the ‘factors of 15’.

On the other hand, the numbers of 15, 30, 45, 60, 75, 90, and so on, are the multiples of 15 respectively. Also, remember that the factors of 15 will divide 15 (once or thrice) without giving a remainder, that is the number will give a division remainder as zero (0).

The number 1 is the smallest known factor for any given integer. Also, if you consider the factors of a number, there are at least (minimum) 2 factors, and the number 1 also accounts for this. When saying that an integer has only 2 factors and having the number 1 itself, then this integer is said to be a ‘prime number’.

We will be learning about 15 as a product of primes using the Prime factorization method in the following sections.

When the Factors of 15 are Taken as Pairs

Considering the factors of 15 together as pairs, it means that 2 numbers are multiplied to get 15 as its product. For example, 1 × 15 gives 15 as its solution. Here, the numbers 1 and 15 are deemed as the factor pairs of ‘15’.

As per this context, when we list all the factors of 15 we get the integers 1, 3, 5 and 15 only. Because 1 × 15 = 15 and 3 × 5 = 15. Hence, considering 15 as a product of primes, only the 4 numbers mentioned are called the factors of 15.

Understanding the Method of Prime Factorisation of 15

Besides having 1 as its divisor, the integer 15 also has other smaller numbers. Hence, 15 is said to be a composite number. Using the Prime Factorization method, we will find out the factors of 15 as given below.

The smallest known prime factor is 2. So, let us divide this number with 15 (15 ÷ 2 = 7.5). Since the answer is a decimal-valued on (7.5), 2 is not considered to be the prime factor of 15.

Let’s move onto the subsequent number, i.e. 3 (15 ÷ 3 = 5). Again, on the division of 5 by 3, we get 5 ÷ 3 = 1.67, which is also a fractional value (1.67).

Lately, let’s divide 5 by the next prime integer which is 5 itself (5 ÷ 5 = 1). As we got the result 1, we are not proceeding with the division of numbers further.

Hence, we are interpreting that the numbers 5 and 3 are the prime factors of 15, in which both 3 and 5 are prime numbers themselves.

Conclusion

The factors of 15 are numbers that when given as the product of 2 integers, results in the same number 15. From the module, 1, 3, 5, and 15 are the list of all the factors of 15. Prime factorization of 15 is the process of decomposing small pieces of integers into a single composite number, which is 15 for our case. This method has also resulted in 1, 3, 5, and 15 as the prime numbers for the composite number 15. The factors of 15, when divided by a number, will not leave any remainder at the end.

FAQ (Frequently Asked Questions)

1. Is there any number with decimal as its factor?

No. Every number should have its factor as a whole number and fractional or decimal values are not allowed. For example, 15 when divided by 2 gives 7.5, which therefore leads to the conclusion that 2 is not the factor of 15.

2. Give the 1st 25 multiplies of the number 15.

The 1st 20 multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, and 375 respectively.

3. Can the Prime factorization method when applied for any other number besides 15 repeats the number?

Yes. At times, you have to write every prime factor for a given number using repetition of the same integer. For example, the prime factorization of the number ‘8’ can be written in the form of 2 × 2 × 2 which gives 8. Hence, number 2 is repeated 3 times in this process.

4. Is there any integer from the number system that has 2 as its factor?

Yes. All the even numbers such as 2, 4, 6, 8, 10, 12, and so on, will have any number of factors but possess 2 as one of its factors. This does not apply to the case of odd numbers.

5. What is that 1 notable feature about the factors of 5?

That 1 notable feature about the factors of 5 is that all the integers that end with the number are said to come with 5 as its factorial value.

6. State the numbers that have 2, 5, and 10 as its factors.

The factors 2, 5, and 10 are possibly seen for any number that is both greater than zero (0) and also ends with the number (0). 20, 40, 80, 70, are some examples to mention.