how can we differentiate between multiples and factors
Answers
Step-by-step explanation:
When a number is said to be a factor of any other second number, then the first number must divide the second number completely without leaving any remainder. In simple words, if a number (dividend) is exactly divisible by any number (divisor), then the divisor is a factor of that dividend. Every number has a common factor that is one and the number itself.
For example, 4 is a factor of 24 i.e. 4 divides 24 exactly giving 6 as quotient and leaving zero as remainder. Alternatively, 6 is also a factor of 24 as it gives 4 as quotient on division. Therefore, 24 has 1, 24, 4, 6 as its factors in addition to 2, 3, 8 and 12 and all these numbers divide 24 exactly leaving no remainder.
If any natural number has only two factors i.e. 1 and the number itself as its factors, such numbers are called prime numbers. 2 is an example of a prime number where it has only two factors 1 and 2.
A multiple of a number is a number that is the product of a given number and some other natural number. Multiples can be observed in a multiplication table. Multiples of some numbers are as follows:
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and so on Hence, multiples of 2 will be even numbers and will end with 0, 2, 4, 6 or 8.
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, and so on.
Multiples of 5 are 5, 10, 15, 20, 25, and so on.
Every multiple of 5 has its last digit as 0 or 5.
In the above-mentioned examples, say multiples of 2, the number 2 can be multiplied by infinite numbers to find the “n” number of multiples. Now, let us assume an example,
3 × 4 = 12
Here, 3 and 4 are the factors of 12,
12 is multiple of 3 and 4
Thus, we can conclude that if X and Y are two numbers and;
• If X divides Y, X is a factor of Y
• If Y is divisible by X, Y is a multiple of X
Since the number 1 divides every integer, it is a common factor of every integer. Also, every number is divisible by 1 and every number is a multiple of 1.
S.No Factors Multiples
1 Factors are defined as the exact divisors of the given number The multiples are defined as the numbers, which is multiplied by the other number to get the result
2 The number of factors is finite The number of multiplies is infinite
3 The operation used to find the factors is a division The operation used to find the multiples is a multiplication
4 The outcome of the factors should be less than or equal to the given number The outcome of the multiples should be greater than or equal to the given number.
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