Page 156 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\07_Chapter_5\Chapter_5
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Divisibility Rules

Finding factors of small numbers is easy but what about the factors of large numbers?
Divisibility rules allow us to quickly check whether a number can be divided by another without
performing long division. Let’s check the rule of divisibility by certain numbers.
Divisibility by 2

A number is divisible by 2 if it ends with 0, 2, 4, 6 or 8. For example, 2346, 6480, 9288 are divisible
by 2.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is also divisible by 3. For example, 234561 is
divisible by 3 as 2 + 3 + 4 + 5 + 6 + 1 = 21 is divisible by 3.
Divisibility by 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example,
148, 45900 and 87632 are divisible by 4 as 48, 00, 32, are divisible by 4.

Divisibility by 5
A number is divisible by 5 if it ends with 0 or 5. For example, 125, 620.

Divisibility by 6

If a number is divisible by both 2 and 3, then it is divisible by 6 also. For example, 1524 is divisible
by 2 as its ones digit is 4. It is also divisible by 3 as 1 + 5 + 2 + 4 = 12 is divisible by 3. So, 1524 is also
divisible by 6.
Divisibility by 7

Subtract twice the last digit (unit
digit) of the number from the Enrichment
remaining number (with the last There is a second rule also on the divisibility of a number by 7.
digit removed). If the result is equal A number ABCDEF......YZ is divisible by 7 if a group of 3 starting
to 0 or is a multiple of 7, then the from the right side is arranged with alternative signs of + and – and
number is divisible by 7. Repeat the the result thus obtained is divisible by 7 then the whole number
process, till you get a 2-digit or 1-digit is divisible by 7.
number to check the divisibility. For example, 1112444333555444666 is divisible by 7.
For example, consider the number As 666 – 444 + 555 – 333 + 444 – 112 + 1 = 777 is divisible by
1561. 7, hence 1112444333555444666 is divisible by 7.
156 – 2 × 1 = 154

15 – 2 × 4 = 7, 7 is divisible by 7.
Hence, 1561 is divisible by 7.
Divisibility by 8

A number is divisible by 8 if the number formed by the last three digits is either divisible by 8 or
is 000. For example, consider the number 4,56,000.

Since the last three digits are 000, hence 4,56,000 is divisible by 8.

Mathematics-6 154