Class 5 Factors and multiples Definations EVEN NUMBERS

Class 5 Factors and multiples

Definations • EVEN NUMBERS : All numbers which are multiples of 2. eg: 2, 4, 6, 8 etc • ODD NUMBERS : All numbers which are not multiples of 2. Eg: 1, 3, 5, 7 etc • PRIME NUMBERS : A number greater than 1 which has only two factors that is 1 and the number itself is called a prime number. EG : 2, 3 , 5 , 7, etc

• COMPOSITE NUMBERS : A number greater than 1 which has more than two factors is called composite number. EX: 4 , 6 , 8 , 9 ETC • TWIN PRIMES : Two numbers with the difference of two are called twin primes. There is a composite number between the Twin primes. EX: 3 and 5 , 5 and 7 , 11 and 13 etc. • CO – PRIME NUMBERS : Two numbers with only 1 as the common factor are called co - prime numbers. Co-prime numbers are not necessarily prime numbers EX: 4 AND 5 , 18 AND 23 etc.

FACTOR TREE Draw a factor tree of 90 90 2 45 2 3 15 2 3 3 5 90 = 2 x 3 x 5

COMMON FACTORS • Ex : Find the common factors of 20 and 45 Sol : factors of 20 = 1 , 2 , 4 , 5 , 10 , 20 factors of 45 = 1, 3, 5 , 9 , 15 , 45 The common factors are = 1 and 5

HCF • The HCF or the highest common factor of two or more numbers is the greatest number (factor ) that exactly divides all the given numbers. • Ex : Find the HCF of 18 and 21 Sol : factors of 18 = 1, 2, 3 , 6 , 9 , 18 factors of 21 = 1, 3 , 7 , 21 common factors are = 1 and 3 The highest of these factors is 3. HCF of 18 and 21 is 3

CLASS - 5 HCF -HIGHEST COMMON FACTOR LCM – LOWEST COMMON MULTIPLE

PRIME FACTORISATION Ex : Find the HCF of 12 and 16 by Prime factorisation method. Sol : 2 12 2 16 2 8 3 3 2 4 1 2 2 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 so, HCF = 2 X 2=4 1 common factor = 2 x 2

LONG DIVISION METHOD FOR TWO NUMBERS Ex : Find the HCF of 32 and 8 Sol : 8 32 4 - 32 0 Thus 8 is the HCF of 32 and 8

LONG DIVISION METHOD FOR THREE NUMBERS Ex : Find the HCF of 45 , 60 and 330 Sol : 45 60 1 15 330 22 - 45 -30 15 45 3 30 - 45 - 30 0 0 Hence the HCF of 45 , 60 and 330 is 15