Divisibility rules are shortcuts or tricks in mathematics that help us quickly check whether a number is divisible by another number without doing the full division.
A number is divisible by 14 if it follows either of these rules.
Rule 1
For a number to be divisible by 14,
- It must be divisible by 2.
The last digit must be an even number.
- It must be divisible by 7.
(Last digit * 2 - remaining digit) is divisible by 7.
If both the conditions are met the given number is divisbile by 14.
For example: Check if 1750 is divisible by 14.
We need to check if the given number 1750 is divisible by 2 and 7, both or not.
- The last digit is an even number. Therefore, 1750 is divisible by 2
- Last digit * 2 - Remaining digit = 0 - 175 = - 175, which is divisible by 7.
Therefore, 1750 is also divisible by 7.
Hence, 1750 is divisible by 14.
Rule 2
For a number to be divisible by 14,
- Take the Last two digits of the number, say a.
- Multiply the remaining digits by 2, say b.
- Sum: a + b.
- If the result is divisible by 14, then the original number is also divisible by 14.
For example: check if 1750 is divisible by 14.
Solution:
- Last two digits = 50
- Twice the remaining digit = 2 x 17 = 34
- Last two digits + Twice the remaining digits = 50 + 34 = 84, which is divisible by 14.
Hence, 1750 is also divisible by 14.
Solved Examples on Divisibility Rule of 14
Example 1: Check whether 266 is divisible by 14.
Using Rule 1:
- Check: Divisibility of 2
Last digit is even therefore it is divisible by 2.- Check: Divisibility of 7
Last digit *2 - remaining digit = 6*2 - 26 = 12 - 26 = -14, which is divisible by 7
Therefore, 266 is divisible by 7.Hence, 266 is divisible by 14.
Using Rule 2:
- Last two digits = 66
- Twice the remaining digits = 2 *2 = 4)
- Last two digits + Twice the remaining digits = 66 + 4 = 70, which is divisible by 14.
Hence, 266 is divisible by 14.
Example 2: Check if 1064 is divisible by 14.
Solution:
Using Rule 1:
We need to check if the given number 1064 is divisible by 2 and 7 both or not
- Last digit is an even number. Therefore, 1064 is divisible by 2
- Last digit * 2 - Remaining digit = 8 - 106 = -98, which is divisible by 7.
1064 is also divisible by 7.Hence, 1064 is divisible by 14.
Using Rule 2:
- Last two digits = 64
- Twice the remaining digit = 2 x 10 = 20
- Last two digits + Twice the remaining digits = 64 + 20 = 84, 84 is divisible by 14.
Hence, 1064 is divisible by 14.
Example 3: Check if 1896 is divisible by 14.
Solution:
Using Rule 1:
We need to check if the given number 1064 is divisible by 2 and 7 both or not
- Last digit is Even number, 126 is divisible by 2.
- Last digit *2 - remaining digit = 12 - 189 = 177, which is not divisible by 7.
Therefore, 1896 is also not divisible by 7.Therefore, 1064 is not divisible by 14.
Using Rule 2:
- Last two digits = 96
- Twice the remaining digit = 2 x 18 = 36
- Add both numbers = 96 + 36 = 132, which is not divisible by 14
Therefore, 1064 is also not divisible by 14.
Unsolved Questions on the Divisibility Rule of 14
Question 1: Check if 322 is divisible by 14 using the divisibility rule.
Question 2: Check if 4368 is divisible by 14 using the divisibility rule.
Question 3: Check whether the number 4379 is divisible by 14 using the divisibility rule.
Question 4: Check whether the number 10292 is divisible by 14 using the divisibility rule.
Question 5: Check whether the number 12345 is divisible by 14 using the divisibility rule.
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