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At the primary level, factors and multiples are two important ideas in mathematics. After dividing a specified integer, a factor is a number that leaves no residue. A multiple, on the other hand, is a number obtained by multiplying two or more numbers. Multiples are unlimited in comparison to factors of a number.
These two appear to be similar at first glance, however, there are several distinctions between factors and multiples that are discussed in this article.
Definition of Factors
The phrase ‘factors’ refers to the numbers that divide a given number precisely, leaving no residue. For example, 2 is one of the many factors of 8 because dividing 8 by 2 yields 4 and leaves no residue. The other 8 factors are 1, 4, and 8.
Furthermore, factors are numbers that can be multiplied by another number to obtain the desired number. Every number has at least two elements, namely 1, and the number itself.
To find the factors of a given number, you must first identify the numbers that evenly divide it. Start with 1 because it is the factor of all numbers.
Definition of Multiples
The multiple of two whole numbers is defined in mathematics as the product of the two whole numbers. For instance, 2 x 4 Equals 8, indicating that 8 is a multiple of 2 and 4. Furthermore, a multiple is indeed a number that, when divided by a certain integer, leaves no residue.
A given number has an infinite number of multiples. Every integer is a multiple of itself and 0
To find multiples of a number, multiply it by integers starting with 1. After multiplying the provided values, the resultant number is a multiple of the original number.
In terms of the differences between factors and multiples, the following points are crucial:
Factors are a set of numbers that divide a given number fully, i.e. they are perfect divisors. Multiples, on the other hand, are a set of numbers that are the products of a single number.
A factor is a number that can be multiplied by another number to produce a new number. Multiples, on the other hand, are the result of multiplying a number by an integer.
The number of factors of a given integer is finite, whereas the number of multiples is infinite.
The number is either less than or equal to the factor. Multiples, on the other hand, are numbers that are bigger than or equal to the provided number.
The division is the operation that is used to find the factors of a given integer. Multiplication, on the other hand, is the method for obtaining multiples of a number.
BASIS FOR COMPARISON | FACTORS | MULTIPLES |
Meaning | The term “factor” refers to the number’s exact divisor. | When we multiply one integer by another, the result is called multiple. |
What is it? | It’s a number that can be multiplied to make a new one. | It’s the result of multiplying an integer by a number. |
The number of factors/multiples | Finite | Infinite |
Outcome | The specified number must be less than or equal to. | The specified number must be greater or equal. |
Operation used | Division | Multiplication |
Example
If two numbers are 2 and 6, and 2 is a factor of 6, then 6 is a multiple of 2. As a result of this explanation, you may have realised that a number is a multiple of all of its factors, such as 6 being a multiple of all of its factors, namely 1, 2, 3, and 6.
Conclusion
A factor is a number that divides a given number without leaving a remainder. A number that can be divided evenly by another number without leaving a residue is called a multiple of that number. Multiples and factors are the polar opposites of each other. We may grasp factors by using a number sentence.
To summarise, factors are numbers that can be multiplied to produce a different number. Multiples, on the other hand, refer to the result of multiplying two numbers. A prime number is one that has only two factors: one and itself.
