Finding out multiples of 15 is not difficult but before getting straight onto it, let us first understand what multiples are. A multiple of a number is the outcome of the product of that number with any other number. In other words, a number that can be divided by another number completely without leaving a remainder is called the multiple of that number. Multiples are usually considered in the form of whole numbers. Here, we will learn about all multiples of 15. Thus, the numbers that we will be focusing on are completely divisible by 15.
A multiple of 15 is a number that can be represented in the form of 15n, where n is any natural number. A number that can be divided a certain number of times by another number is called the multiple of the other number. Suppose we have two numbers M and N.
M is said to be the multiple of N if, M = nN, where n stands for natural numbers.
Some common multiples of 15 are:
30, 45, 60, 75, 225 etc.
The numbers that are products of 15 or can be divided by 15 without leaving a remainder are multiples of 15. By looking at the equation, one can easily identify multiples as well as factors of a given number. For example, 30, 45, 60, 75 and 225 are all common multiples of 15 pertaining to the following arrangement of equations:
These are all represented as multiples as they are procured by adding or subtracting original number i.e. 15, multiple times.
Common multiples of 15 chart looks something like this:
The 9th multiple of 15 is to be found multiplying 15 by 9, such that:
15 x 9 = 135
Thus, the ninth multiple of 15 is 135.
The Least Common Multiple is also referred to as Lowest Common Multiple or Least Common Divisor. If there are two integers a and b, in that case, the smallest positive integer that is evenly divisible by both a and b is the least common multiple of a and b.
Suppose there are two numbers 15 and 3, the LCM (15,3) = 15
The LCM of two or more numbers is the smallest number that is divisible by the whole set of numbers without leaving a remainder.
Just like the multiples of 15 are 15, 30, 45, 60, 90, 225 and so on, on the contrary 1, 2, 3, 4, 6 and 15 are factors of 15.
Multiples and factors are often confused by people for one of the other. But they are not the same!
The numbers that can completely divide a number without leaving a remainder are called the factors of that specific number. The basic concept is that 15 is one of the multiples of the factors of 15.
For example, 7 is a factor of 14, i.e.7 completely divides 14 without leaving a remainder and having a quotient of 2. Conversely, 2 is also a factor of 14 as it gives 7 as quotient on division. Thus, 14 has factors 2, 7, 14 and 1 which divide 14 without leaving any remainder.
On the other hand, 14 is a multiple of 2 as well as a multiple of 7.
7 x 2 = 14
Factor of 14 Factor of 2 Multiple of 7 or 2
The basic difference between factors and multiples are:
Q1. Mention Some of the Multiples of 15 Between 100 and 1000.
Ans: There are as many as 58 multiples of 15 between 100 and 1000. Some of the randomly chosen multiples are 105, 180, 300, 375, 465, 540, 600, 660, 735, 810, 855, 900, 930, and 990. For solving big numerical problems in less time, it is advisable to memorise some multiples of 15 between 100 and 1000 or do the division at a lightning-fast speed. ‘Practice’ is the only way how one can keep building his stock of multiples for a particular number.
Q2. What is the Basic Difference Between a Prime Number and a Composite Number?
Ans: Prime numbers have only two factors that are 1 and itself. As they do not have any other factors, we can say that they cannot be factored. For example, 11 is a prime number (as it has two factors 1 and 11 only). It could also be expressed as a product of other real numbers in various combinations.
Composite numbers are numbers except for prime number 1, which have more factors other than 1 and itself and can be factored using a combination of different whole numbers. For example, 18 can be factored as 3 × 6, or as 9 × 2, or as 2 × 3 × 3. All composite numbers cannot be factored by more than one combination. For example, 14 can be factored only as 7 × 2.