Page 99 - Math Genius C4

E:\Working\Orange_Education\Math_Genius_4\Open_Files\Chap-05
\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Divisibility by 4 2. Using the divisibility rules, check whether the following numbers are divisible by 2,
rule: A number is divisible by 4 if the number formed by the two extreme right 3, 4, 5, 9 or 10. Write ‘Yes’ if the number is divisible and ‘No’, if it is not divisible.

digits is divisible by 4 or the last two digits are zeros. Divisible by
Examples: (a) 148 is divisible by 4 because 48 ÷ 4 = 12 Numbers 2 3 4 5 9 10

(b) 3100 is divisible by 4 because the last two digits are 00. (a) 62
96
Divisibility by 5 (b) 284
(c)
rule: A number is divisible by 5 if the number ends with 5 or 0. (d) 251
Examples: 95 and 130 are divisible by 5. (e) 1024

Divisibility by 6 (f) 6318

rule: A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 54 is divisible by 2 as its ones digit is 4. maths fun Art Integration

54 is also divisible by 3 as the sum of digits 5 + 4 = 9 and 9 ÷ 3 = 3. A balloon seller has three bunches of balloons. There is a number
written on each balloon. Colour the balloon as per the code given.
So, 54 is divisible by 6 as well. If the number is divisible by 2905 330 3240
Divisibility by 9 � 2 only — Colour green 405 3438 1738

rule: This is similar to divisibility by 3. If the sum of the digits of a number is � 5 only — Colour yellow 1430 635 565 3225 1306 480 882 1965 3080
divisible by 9, then the number itself is divisible by 9. � 2, 5 and 10 — Colour red 2270 1116 1940 1914 295 3894

Example: In 63, 6 + 3 = 9 and 9 ÷ 9 = 1 Now, answer the following: Bunch A Bunch B Bunch C
So, 63 is divisible by 9. 1. Which bunch has the maximum number of yellow balloons?

Divisibility by 10 2. Are there more green balloons or red balloons?

rule: Numbers ending in 0 are divisible by 10.
Examples: 80, 500, 1530 are divisible by 10. PriMe NUMBers aND coMPosite NUMBers
Let us find the factors of numbers from 1 to 10.

Think Tank Logical Thinking Numbers 1 2 3 4 5 6 7 8 9 10
Check if your area PIN Code is divisible by 2, 3 and 5. Factors 1 1, 2 1, 3 1, 2, 4 1, 5 1, 2, 3, 6 1, 7 1, 2, 4, 8 1, 3, 9 1, 2, 5, 10

Number of factors 1 2 2 3 2 4 2 4 3 4

Practice time 5c Here, we can observe that

1. State whether the following statements are true (T) or false (F). � The number 1 has only 1 factor, which is itself.
� Numbers 2, 3, 5 and 7 have exactly two factors, that is, 1 and the number itself.
(a) 243 is divisible by both 9 and 3.
These numbers are called prime numbers.
(b) A number that is divisible by 5 is also divisible by 10. Be Aware
Numbers which have exactly two factors, 1 and 1 is the only number which
(c) A number that is divisible by 6 will always be divisible by 3. the number itself, are called prime numbers. is neither a prime nor a
composite number.
(d) If the sum of the digits of any number is a multiple of 9, the number is � The numbers 4, 6, 8, 9 and 10 have more than two factors. These numbers are
divisible by 3.
called composite numbers.

Mathematics-4 97