Page 54 - Start Up Mathematics_6

Test of divisibility by 10
A number is divisible by 10, if the digit at its ones place is 0.
The numbers 20; 30; 300; 560 and 56,780 are divisible by 10 as the digit at ones place in these
numbers is 0. However, the numbers 35; 568 and 15,805 are not divisible by 10.

Test of divisibility by 5
A number is divisible by 5, if the digit at its ones place is either 0 or 5.
The numbers 10; 15; 20; 25; 300; 565 and 56,780 are divisible by 5 as the digit at ones place in
these numbers is either 0 or 5. However, the numbers 752; 3,608 and 17,414 are not divisible by 5.

Test of divisibility by 2

A number is divisible by 2, if it has any of the digits 0, 2, 4, 6 or 8 at its ones place.
The numbers 10; 12; 24; 126; 258; etc. are divisible by 2 as the digit at ones place in these numbers
is 0, 2, 4, 6, or 8. However, the numbers 25; 761 and 4,083 are not divisible by 2.

Test of divisibility by 3
A number is divisible by 3, if the sum of its digits is a multiple of 3.
The number 12,93,006 is also divisible by 3 as 1 + 2 + 9 + 3 + 0 + 0 + 6 = 21 is a multiple of 3.
The number 21,00,008 is not divisible by 3 as 2 + 1 + 0 + 0 + 0 + 0 + 8 = 11 is not a multiple of 3.

Test of divisibility by 6

A number is divisible by 6, if it is divisible by both 2 and 3.
The number 12,936 is divisible by 2 as it has 6 at its ones place. In addition, 12,936 is also divisible
by 3 as 1 + 2 + 9 + 3 + 6 = 21 is a multiple of 3. Therefore, 12,936 is divisible by 6.

Test of divisibility by 4
A number with three or more digits is divisible by 4, if the number formed by its last two digits
(i.e., tens and ones place) is divisible by 4.

The number 312 is divisible by 4 as 12 is divisible by 4.
The number 64,121 is not divisible by 4 as the number formed by its last two digits (i.e., tens and
ones place) is 21, which is not divisible by 4.

Test of divisibility by 8
A number with four or more digits is divisible by 8, if the number formed by its last three digits
(i.e., hundreds, tens and ones place) is divisible by 8.

The number 7,85,064 is divisible by 8 as 064 is divisible by 8.
The number 53,644 is not divisible by 8 as the number formed by its last three digits, i.e., 644 is
not divisible by 8.

To check the divisibility of numbers having up to 3 digits by 8, actual division is to be carried out.
Test of divisibility by 9

A number is divisible by 9, if the sum of its digits is divisible by 9.
The number 35,064 is divisible by 9 as 3 + 5 + 0 + 6 + 4 = 18 is divisible by 9.
The number 72,937 is not divisible by 9 as 7 + 2 + 9 + 3 + 7 = 28 is not divisible by 9.

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