Page 81 - Maths Class 04
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Divisibility Properties of Numbers
A number is said to be divisible by another number, if on dividing the number
by the other, the remainder is zero.
Divisibility by 2 Divisibility by 3
Every even number is divisible by 2. A number is divisible by 3 if the sum
For example : 4, 12, 16, 102, 300, 496 of its digits is multiple of 3 or
are even numbers. So, they are divisible by 3.
divisible by 2. For example : Consider a number 27.
Sum of 2 and 7 is 2 + 7 = 9
9 is a multiple of 3. Thus, 27 is divisible
by 3. (27 ÷ 3 = 3)
Divisibility by 4 Divisibility by 5
A number is divisible by 4 if it has A number is divisible by 5 if it has
zeros at units and tens places or the either ‘0’ or ‘5’ at its ones (unit) place.
numbers formed by the last two For example : 160 is divisible by 5
digits, from its extreme right is because there is 0 at ones place.
divisible by 4. (160 ÷ 5 = 32)
For example : 500 is divisible by 4 2165 is divisible by 5 because there is
because it has 0 at unit and tens 5 at ones place.
places respectively. (2165 ÷ 5 = 433)
Divisibility by 6 Divisibility by 7
Every even number that is divisible A number is divisible by 7 if the
by 3 is also divisible by 6. difference between the twice of the
For example : 162 is divisible by 3. number at ones place and the
So, it is divisible by 6. number formed by the remaining
(162 ÷ 6 = 27) digits is either zero or multiple of 7.
309 is divisible by 3 but it is an odd. For example : 42 is divisible by 7.
So, it is not divisible by 6. Here, 4 – (2 × 2) = 4 – 4 = 0
406 is even but it is not divisible by Hence, 42 is divisible by 7.
3. So, it is not divisible by 6. (42 ÷ 7 = 6)
Mathematics-4 81
