What are Factors and Multiples?
Factors & Multiples
Factors
The numbers that we multiply to get a certain number are called its factors.
For example, 2 × 5 = 10
Here, both 2 and 5 are factors of 10.
In the above example, we can see that 2 and 5 both can completely divide 10 without leaving any remainder.
So, we can say that factors are “all of those numbers”that can divide “a given number” completely (meaning – the remainder should be 0 after division).
Example - Write all the factors of 12.
Factors of 12 are 1, 2, 3, 4, 6 and 12 as each of these can completely divide 12.
Multiples
Are the numbers we get when we multiply any counting number by an integer, and are called its multiples.
For example,6 × 5 = 30
6 × 7 = 42
Here, both 30 and 42 are multiples of 6.
We can see in the above example, 30 is a multiple of 5 too and 42 is a multiple of 7 too. So, we can say 30 is a common multiple of 5 and 6, and 42 is a common multiple of 6 and 7.
Example- Write 5 multiples of 12.
Multiples of 12 are 12, 24, 36, 48, 60.
Do Remember
#Factors and multiples are inter-related with each other. Every number is a factor of its multiple.
Example- If 18 is a multiple of 6, then 6 is a factor of 18.
Prime Factorization
When we express a composite number as a product of prime numbers, it is called prime factorization. The set of prime numbers are called the prime factors of the given number.
Example-Let us take a number 24.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.
Out of these factors, the prime factors are 2 and 3.
Now, let us express 24 as a product of its prime factors.
So, 24 = 2 × 2 × 2 × 3
Thus, prime factorization is expressing a number as a product of its prime factors.
Method 1: Factor Tree Method
In this method, we start splitting the given numbers into factors until we cannot split anymore.
The factor that cannot be split anymore i.e. the prime factor is carried down as it is whereas the composite factor is further split in the next step till it becomes prime.
Then, all the prime factors of the number are stated in product form to define the actual number.
The standard way of listing the prime factors is from smallest number to the largest one.
Example – Find the prime factorization of 60.
Thus, 60 = 2 × 2 × 3 × 5
#The given number can be treated as a stem while its breakup into prime factors can be treated as its branches.
Method 2:Short Division Method
In this method, first we divide the given number by a smallest prime number which completely divides the given number.
Then, we divide the quotient again with a smallest prime number or the next smallest prime number which can completely divide the number.
We repeat the above step again and again, till the quotient becomes 1.
The product of all the divisors that we got through the above step gives us the number itself and are thereby the prime factors of the number.
Example – Find the prime factorization of 72.
Thus, 72 = 2 × 2 × 2 × 3 × 3
Related Articles
5th Grade, Module 3: What is HCF and LCM?
H.C.F. AND L.C.M. Factors of a number are exact divisors of that number. But what is the use of such concepts in real life? These concepts are used in arranging things. It helps in the arrangements of items into rows and columns. In this chapter we ...What is Prime Factorization?
Prime Factorization When we express a composite number as a product of prime numbers, it is called prime factorization. The set of prime numbers are called the prime factors of the given number. Example-Let us take a number 24. Factors of 24 = 1, 2, ...How is Time Related to Math?
We often use the following phrases- classroom time table break time time of each period time to go to school school over time time to sleep time to go to play The common thing that we can see here is the word ‘time’. Let us learn more about the ...5th Grade, Module 14: How does Temperature Relate to Math?
TEMPERATURE Temperature is a very common term that we use in our daily life directly or indirectly whenever we say that today’s temperature is too high or the ice-cream is too cold or while we measure our body temperature. In this chapter we will ...5th Grade, Module 12: What is a Bill in Math?
BILL of Purchase a.k.a BILL By reading the chapter’s name the very first thing comes to our mind is the money we pay. When we go to restaurants, purchase grocery for home or buy stationary for school, we pay the bill at the end. Bills are an ...