Divisible by 6
Divisible by 6 is discussed below:
Consider the multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, .........
All the multiples end with 2, 4, 6, 8 or 0.
Hence, these are divisible by 2.
|
Number |
Sum of the Digits |
|
12 18 24 48 54 |
1 + 2 = 3 1 + 8 = 9 2 + 4 = 6 4 + 8 = 12 5 + 4 = 9 |
Since the sums of the digits of all these multiples are divisible by 3, they are divisible by 3.
Numbers which are divisible by both 2 and 3 are divisible by 6.
1. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156.
(i) 42
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
42 is divisible by 2. Since the unit place is 2 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
42 is divisible by 3. Since the sum of the digits of 42 = 4 + 2 = 6 which is divisible by 3.
Therefore, 42 is divisible by both 2 and 3.
Hence, 42 is divisible by 6.
(ii) 144
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
144 is divisible by 2. Since the unit place is 4 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
144 is divisible by 3. Since the sum of the digits of 144 = 1 + 4 + 4 = 9 which is divisible by 3.
Therefore, 144 is divisible by both 2 and 3.
Hence, 144 is divisible by 6.
(iii) 180
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
180 is divisible by 2. Since the unit place is 0, divisible by 2.[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
180 is divisible by 3. Since the sum of the digits of 180 = 1 + 8 + 0 = 9 which is divisible by 3.
Therefore, 180 is divisible by both 2 and 3.
Hence, 180 is divisible by 6.
(iv) 258
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
258 is divisible by 2. Since the unit place is 8 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
258 is divisible by 3. Since the sum of the digits of 258 = 2 + 5 + 8 = 15 which is divisible by 3.
Therefore, 258 is divisible by both 2 and 3.
Hence, 258 is divisible by 6.
(v) 156
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
156 is divisible by 2. Since the unit place is 6 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
156 is divisible by 3. Since the sum of the digits of 156 = 1 + 5 + 6 = 12 which is divisible by 3.
Therefore, 156 is divisible by both 2 and 3.
Hence, 156 is divisible by 6.
2. Consider the following numbers which are not divisible by 6, using the rules of divisibility by 6: 70, 135, 184, 286, 297.
Note: A number is divisible by 6 if it is divisible by 2 and 3 both.
(i) 70
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
70 is divisible by 2. Since the unit place is 0 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
70 is not divisible by 3. Since the sum of the digits of 70 = 7 + 0 = 7 which is not divisible by 3.
Therefore, 70 is divisible by 2 but not by 3.
Hence, 70 is not divisible by 6.
(ii) 135
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
135 is not divisible by 2. Since the unit place is 5, which is not divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
135 is divisible by 3. Since the sum of the digits of 135 = 1 + 3 + 5 = 9 which is divisible by 3.
Therefore, 135 is divisible by both 3 but not by 2.
Hence, 135 is not divisible by 6.
(iii) 184
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
184 is divisible by 2. Since the unit place is 4 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
184 is not divisible by 3. Since the sum of the digits of 184 = 1 + 8 + 4= 13 which is not divisible by 3.
Therefore, 184 is divisible by 2 but not by 3.
Hence, 184 is not divisible by 6.
(iv) 286
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
286 is divisible by 2. Since the unit place is 6 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
286 is not divisible by 3. Since the sum of the digits of 286 = 2 + 8 + 6 = 16 which is not divisible by 3.
Therefore, 286 is divisible by 2 but not by 3.
Hence, 286 is not divisible by 6.
(v) 297
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
297 is not divisible by 2. Since the unit place is 7, which is not divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
297 is divisible by 3. Since the sum of the digits of 297 = 2 + 9 + 7 = 18 which is divisible by 3.
Therefore, 297 is divisible by both 3 but not by 2.
Hence, 297 is not divisible by 6.
3. Is 8622 divisible by 6?
The number ends in 2. Hence it is divisible by 2.
Sum of the digits = 8 + 6 + 2 + 2 = 18, is divisible by 3.
Hence 8622 is divisible by 6.
We can verify that 8622 is divisible by 6 by actual division.
Questions and Answers on Divisible by 6:
1. Which of the following numbers are divisible by 6?
(i) 258
(ii) 96420
(iii) 3448
(iv) 1360
(v) 4008
(vi) 771
(vii) 11190
(viii) 6124
Answer:
2. (ii) 96420
(v) 4008
(vii) 11190
Problems on Divisibility Rules
Worksheet on Divisibility Rules
5th Grade Math Problems
From Divisible by 6 to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Fundamental Geometrical Concepts | Point | Line | Properties of Lines
Apr 18, 24 02:58 AM
The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples. -
What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral
Apr 18, 24 02:15 AM
What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments. -
Simple Closed Curves | Types of Closed Curves | Collection of Curves
Apr 18, 24 01:36 AM
In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves. -
Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles
Apr 18, 24 12:31 AM
Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o… -
Time Duration |How to Calculate the Time Duration (in Hours & Minutes)
Apr 17, 24 01:32 PM
We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.