Maths, FactorsAndMultiples, class 6
Composite Numbers
Numbers having more than two factors are known as composite numbers.
Prime Numbers
Numbers which have exactly two factors, namely 1 and itself.
(Properties of HCF and LCM) -5
The HCF of a group of numbers is always a factor of their LCM.
(Properties of HCF and LCM) -1
The HCF of a group of numbers is not greater than any of the given numbers.
(Properties of HCF and LCM) -2
The HCF of two co-primes is 1
(Properties of HCF and LCM) -3
The LCM of a group of numbers is not less than any of the given numbers.
(Properties of HCF and LCM) -4
The LCM of two co-primes is equal to their product.
HCF ( Highest Common Factor)
The greatest number which is a common factor of two or more given numbers. Find HCF by prime factorization. Find HCF by division
LCM ( Least Common Multiple)
The lowest common multiple of two or more numbers is the smallest number which is a multiple of each of the numbers. Finding LCM by prime factorization Finding LCM by division.
(true / false) 1 is neither prime nor composite
True
(true/false) 2 is the lowest prime number
True
(true/false) 2 is the only even prime number. All other even numbers are composite numbers.
True
(true/false) If a number divides two numbers exactly, it must divide their sum exactly.
True
(true/false) Two prime numbers are always co-primes.
True
Two co-primes need not be prime numbers
True
Twin Primes
Two consecutive odd prime numbers are known as twin primes. Example : (3,5) (5,7) (11,13)
CO-PRIMES
Two numbers are said to be co-primes if they do not have a common factor other than 1. Example:- (2,3) (4,9) (8,15)
(true/false) 1 is the smallest prime number
false
(true/false) A number is divisible by 18, if it is divisible by both 3 and 6.
false
(true/false) If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
false
(true/false) If a number is divisible by 4, it must be divisible by 8.
false
(true/false) If a number is prime. It must be odd.
false
(true/false) If two numbers are co-primes, atleast one of them must be a prime number.
false
(true/false) Sum of two prime numbers is always a prime number
false
(Application of HCF) Find greatest number which divide number x and y leaving the remainder a and b.
find HCF of (x-a) and (y-b)
Test of divisibility by 10
if its ones digit is 0
Test of divisibility by 5
if its ones digit is 0 or 5
Test of Divisibility by 2
if its ones digit is 0,2,4,6 or 8
Test of Divisibility by 3
if sum of its digits is divisible by 3
Test of divisibility by 11
if the difference of the sum of its digits in odd places and the sum of its digits in even places is either 0 or a multiple of 11.
Test of Divisibility by 4
if the number formed by its digits in the tens and ones places is divisible by 4. Example 96852 is divisible by 4 as 52 is divisible by 4.
Is there any counting number having no factor at all ?
no
(true/false) If a number is divisible by 3 and 7, it must be divisible by 21.
true
(true/false) If a number is divisible by 8, it must be divisible by 4.
true
(true/false) If a number is divisible by both 9 and 10, it must be divisible by 90.
true
(true/false) Sum of two consecutive odd numbers is always divisible by 4.
true
Prime Factor
A factor of a given number is called a prime factor, if this factor is a prime number.
Factor
A factor of a number is an exact divisor of than number.
Multiple
A number is said to be a multiple of any of its factors.
Prime Triplet
A set of three consecutive prime numbers differing by 2 is called a prime triplet. The only prime triplet is (3,5,7).
How you will find HCF of more than two numbers.
Choose any two numbers find their HCF. Now HCF of this HCF and third number gives the HCF of these three numbers.
(Application of HCF) Reduce fraction a/b to its lowest terms
Find HCF of a and b and then divide both a and b by HCF.
(Properties of HCF and LCM) -6
If a and b are two given numbers such that a is factor of b then their HCF =a and LCM=b
Properties of Divisibility - 4
If a number is a factor of each of the two given numbers then it must be a factor of their difference.
Properties of Divisibility -1
If a number is divisible by another number, it must be divisible by each of the factors of that number.
Properties of Divisibility -2
If a number is divisible by each of two co-prime numbers, it must be divisible by their product.
Properties of Divisibility -3
If a number is factor of each of the two given numbers, then it must be factor of their sum.
Test of divisibility by 6
If it is divisible by each one of 2 and 3.
Test of divisibility by 7
If the difference between twice the ones digit and the number formed by the other digits is either 0 or a multiple of 7.
Test of divisibility by 8
If the number formed by its digits in hundreds, tens and ones is divisible by 8.
Perfect Numbers
If the sum of all the factors of a number is two times the number, then the number is called a perfect number. Example :- 6 and 28
Test of divisibility by 9
If the sum of its digits is divisible by 9
(Properties of HCF and LCM) -7
If two numbers are given then the product of the two numbers = the product of their HCF and LCM.
