Properties of Factors

Roy and Ram were two close friends. Roy has 6 chocolates and decided to share equally with Ram.

So, Roy gave 3 chocolates to Ram and kept remaining 3 with him

But another friend Sam joined them now they wanted to share the chacolates among them equally

And now the friends have 2 chocolates each

But when another friend Suraj joined them

Roy was unable to share the chocolates among 4 friends equally

To understand why this happned we need to learn about factors

When 6 is divided by 1,2 , 3 or 6 the remainder is zero.

But when 6 is divided by 4 and 5, the remainders are 2 and 1 and hence are not factors of 6

This why Roy was not able to share 6 chacolates among 4 friends equally

Properties of Factors

1) 1 is a factor of every number.

This is because 1 divides every number leaving a reaminder 0

2) Every number is a factor of itself.

The remainder is zero when a number is divided by itself

3) Every factor of a number is an exact divisor of that number.

Factors of 4 are 1, 2 and 4 and are exact divisors of 4.

3) Every factor is less than or equal to the given number

All factors of 34 are less than or equal to 34

4) Number of factors of a given number are finite.

Highest Common Factor of two numbers

The greatest of all common factors of given number is called Highest common factor (HCF) of the numbers

Find the common factors for above numbers,

All the factors of 15 are as shown,

Similarly, all the factors of 20 are as shown,

Thus, common factors in 15 and 20 are as shown,

Out of these two common factors the highest or greatest common factor is 5

So 5 is the HCF of 15 and 20

Properties of HCF

1) HCF of two or more numbers cannot be greater than any of them

Highest Common factor of 32 and 48 is 16 which are less than both the numbers,

2) If a number is factor of another number, then their HCF is the smallest number.

HCF of 8 and 32 is 8 as shown,

Revision

HCF of two or more numbers cannot be greater than any of them.

If a number is factor of another number, then their HCF is the smallest number.

The End