Download factor and multiple factor multiple

FACTOR AND MULTIPLE
FACTOR
If a number is exactly divisible by another number, then the second number is called the
FACTOR of the first number.
Ex: 4 is divisible by 2, then 2 is called FACTOR of 4.
So, a FACTOR of a number is an exact divisor of that number.
Ex: 1,2,3 and 6 are exact divisors of 6.
So, 1,2,3 and 6 are factors of 6. But 4 and 5 are not the FACTORS of 6.
MULTIPLE
A MULTIPLE of a number is a number obtained by multiplying it by a natural number.
Ex: 3, 6, 9, 12, 15, 18, …….. are MULTIPLES of 3.
So, if a number is a factor of another number, then the bigger number is called the MULTIPLE of
the smaller number.
Ex: If 2 is a factor of 4, then 4 is MULTIPLE of 2.
PROPERTIES
FACTOR
MULTIPLE
Factors of a given number are finite.
Multiples of a given number are infinite.
1 is a factor of every number.
1 is not a multiple of every number.
Every number is a factor of itself.
Every number is a multiple of itself.
The greatest factor of a number is that
The lowest multiple of a number is that
number itself.
number itself.
Every factor of a number is an exact divisor of Every number is a multiple of each of its
that number.
factor.
Every factor of a number is less than or equal
Every multiple of a number is greater than or
to that number.
equal to that number
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HIGHEST COMMON FACTOR (HCF)
The HCF of two or more numbers is the largest number that devides all the given numbers.
Ex: HCF of 24 and 36
Factors of 24 – 1, 2, 3, 4, 6, 8, 12 and 24
Factors of 36 – 1, 2, 3, 4, 6, 9, 12 and 36
Now Common Factors – 1, 2, 3, 4, 6 and 12
So, Highest Common Factor is 12.
Trick:
2 24, 36
2 12, 18
3 6, 9
2, 3
So, HCF of 24 and 36 = 2x2x3 = 12 (Multiplication of extreme left numbers)
LEAST COMMON MULTIPLE (LCM)
The LCM of two or more numbers is the smallest number which is divisible by all the given
numbers.
Ex: LCM of 8 and 12
Multiples of 8 – 8, 16, 24, 32, 40, 48, 56, 64, 72, …………..
Multiples of 12 – 12, 24, 36, 48, 60, 72, …………….
No Common Multiples are 24, 48, 72, ………………
So, Lowest Common Multiple is 24.
Trick:
2 8, 12
2 4, 6
2, 3
So, LCM of 8 and 12 = 2x2x2x3 = 24 (Multiplication of extreme left and bottom numbers.)
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Note:
 The product of HCF and LCM of two numbers (Not more than two numbers) is equal to the
product of those numbers.
 The HCF of any two prime or co-prime numbers is equal to 1.
 The LCM of any two prime or co-prime numbers is equal to their product.
 The HCF of two or more numbers is never greater than any of those numbers.
 The LCM of two or more numbers is never less than any of those numbers.
 The HCF of two or more numbers is a factor of their LCM.
 If m is a factor of n, then HCF of m and n is m and LCM of m and n is n.
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