Page 51 - Start Up Mathematics_5

6 Make a factor tree for the following numbers.

(a) 24 (b) 98 (c) 111 (d) 132

7 Write the following numbers as the product of their prime factors. Use division method.

(a) 242 (b) 156 (c) 500 (d) 750

Tests of Divisibility

A number is divisible by 2, if it is an even number, i.e., the digit at its ones
Divisibility by 2
place is 0, 2, 4, 6 or 8.

Divisibility by 3 A number is divisible by 3, if the sum of its digits is divisible by 3.

A number is divisible by 4, if its last two digits are either 0 or the number
Divisibility by 4
formed by them is divisible by 4.

Divisibility by 5 A number is divisible by 5, if the digit at its ones place is 0 or 5.

Divisibility by 6 A number is divisible by 6, if it is divisible by both 2 and 3.

A number is divisible by 8, if the last three digits are either 0 or the number
Divisibility by 8
formed by them is divisible by 8.

Divisibility by 9 A number is divisible by 9, if the sum of its digits is divisible by 9.

Divisibility by 10 A number is divisible by 10, if the digit at its ones place is 0.

A number is divisible by 11, if the difference between the sum of the digits
Divisibility by 11 at odd places and the sum of the digits at even places is either 0 or a
number divisible by 11.

Example 1: Is 45,748 divisible by 2?
Solution: In 45,748, the digit at the ones place is 8 which is an even number. So, 45,748
is divisible by 2.

Example 2: Is 2,437 divisible by 3?
Solution: Sum of digits in 2,437 = 2 + 4 + 3 + 7 = 16

16 is not divisible by 3. So, 2,437 is not divisible by 3.

Example 3: Check the divisibility of the following numbers by 4.
(a) 93,700 (b) 4,12,632
Solution: (a) Since the last two digits of 93,700 are zeros, it is divisible by 4.

(b) The number formed by the last two digits of 4,12,632 is 32, which is
divisible by 4.
So, 4,12,632 is also divisible by 4.

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