Question

6. Apply the divisibility rule and show that
(e) 8,46,300 is divisible by 6.​

Answer 1

Answer:

Divisible By" means "when you divide one number by another the result is a whole number"

Examples:

14 is divisible by 7, because 14 ÷ 7 = 2 exactly

15 is not divisible by 7, because 15 ÷ 7 = 2 17 (the result is not a whole number)

0 is divisible by 7, because 0 ÷ 7 = 0 exactly (0 is a whole number)

"Divisible by" and "can be exactly divided by" mean the same thing

The Divisibility Rules

These rules let you test if one number is divisible by another, without having to do too much calculation!

Example: is 723 divisible by 3?

We could try dividing 723 by 3

Or use the "3" rule: 7+2+3=12, and 12 ÷ 3 = 4 exactly Yes

Note: Zero is divisible by any number (except by itself), so gets a "yes" to all these tests.

1

Any integer (not a fraction) is divisible by 1

2

The last digit is even (0,2,4,6,8)

128 Yes

129 No

3

The sum of the digits is divisible by 3

381 (3+8+1=12, and 12÷3 = 4) Yes

217 (2+1+7=10, and 10÷3 = 3 1/3) No

This rule can be repeated when needed:

99996 (9+9+9+9+6 = 42, then 4+2=6) Yes

4

The last 2 digits are divisible by 4

1312 is (12÷4=3) Yes

7019 is not (19÷4=4 3/4) No

A quick check (useful for small numbers) is to halve the number twice and the result is still a whole number.

12/2 = 6, 6/2 = 3, 3 is a whole number. Yes

30/2 = 15, 15/2 = 7.5 which is not a whole number. No

5

The last digit is 0 or 5

175 Yes

809 No

6

Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)

114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No

7

Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7. (We can apply this rule to that answer again)

672 (Double 2 is 4, 67−4=63, and 63÷7=9) Yes

105 (Double 5 is 10, 10−10=0, and 0 is divisible by 7) Yes

905 (Double 5 is 10, 90−10=80, and 80÷7=11 3/7) No

8

The last three digits are divisible by 8

109816 (816÷8=102) Yes

216302 (302÷8=37 3/4) No

A quick check is to halve three times and the result is still a whole number:

816/2 = 408, 408/2 = 204, 204/2 = 102 Yes

302/2 = 151, 151/2 = 75.5 No

9

The sum of the digits is divisible by 9

(Note: This rule can be repeated when needed)

1629 (1+6+2+9=18, and again, 1+8=9) Yes

2013 (2+0+1+3=6) Not

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