This is Session 3 of the Chapter: Factors and Multiples from Class 5 CBSE Maths.
In this session, Shashank Sir will take you through the following topics from the chapter: Factors and Multiples Class 5 Maths:
✖Divisibility of Numbers
✖Common Factors
✖Common Multiples
✖Co-prime Numbers
✖Other Divisibility rules
✖Prime Factorization
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Factors and Multiplies
TEST OF DIVISIBLITY
•Number divisible 2 are called even numbers. They have 0,2,6,8 in units place.
•A number divisible by 3, if the sum of all digits is divisible by3.
o Example: 1563= 1+5+3+6=15. [3 x5=15]
•A number divisible by 4, if the number formed by its ones and tens in tens place is divisible by 4 are00.Example: 1688 [88\4=22]
•A number is divisible by 5 if its units place is either 0 or 5. Eg:790
•A number is divisible by 6 only if its divisible 2 or3
•A number is divisible by 8 if the number formed by last three digits is either 000 or 8.
•A number is divisible by 9 if sum of all its digit is divisible by 9
•A number is divisible by 10 if its ones digit is 0
•A number is divisible by 11 if the difference of all sum its alternate digits is either 0 or multiple of 11.
•A number is divisible by 12 if it is divisible by 3 as well as 4.
•A number is divisible by 15 if its divisible by 3 as well 5.
FACTORS
Activity:
You have 2 toffees. You have to arrange them in group of equal numbers. What you can do is: arrange these 2 toffees in 1 group of 2 toffees;
Or arrange them in 2 groups of 1 toffee each. Hence, 2=1x22=1x2Thus,2=1x2=2x1
•From the above discussion, in a division when there is no remainder, the quotient re factors of thedividend.
•1 is a factor of every number.
•A number is a factor ofitself.
•1 is the smallest factor o everynumber.
PERFECT NUMBER:
A perfect number is a number whose sum of all factors is twice the number.
LISTING FACTORS OF GIVEN NUMERS
➢Unique number
➢Prime number
➢Prime
➢Composite number
➢Prime number
•All the numbers with only two factors are called prime numbers.
•All the numbers with more than two factors are called composite numbers.
MULTIPLES
Multiples is a number that contains another number for exact number of times.
Example:
10 is a multiple of 2
12 is a multiple of 3
15 is a multiple of 5
Observation: Every number is multiple of 1. Multiples are infinite. Every number is a multiple of itself. To find multiples of a number in an ascending order we multiply it by 1,2,3,4, etc.
Exploring Multiplies to learn prime factorization of composite numbers.
All natural numbers are classified in to prime and composite.
o A number which has only 2 different factors, 1 and the number itself is a prime number. Eg:2,3,5,7,11,13
o A natural number which has more than two different factors is a composite number. Eg: 4, 6, and8,9,10.
o 1 is neither a prime number nor a composite number because it only one factor. It is a special natural number.
The process of decomposition of a composite number into prime factors is known as factorization.
For example-30=2x3x5Every composite number has one and only one prime factorization.
MAGIC PRIME NUMBERS: 2, 3, 7.
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