A number (say N1) is divisible by another number (say N2) if the remainder is zero when N1 is divided by N2 (Example 18/9 = 2, with a remainder of 0, so 18 is divisible by 9). Have you ever found it difficult to check if a number is divisible by 7, 13 and 17? If yes, do not worry! Here are some easy rules to find out if a number is divisible by these numbers.
Divisible by 7:
To check if a number is divisible by 7 just follow these simple steps:
- Double the last digit of the original number and subtract it from the truncated number.
- Apply step 1 over and over multiple times until you get a single digit or a double digit value.
- If the resultant value is divisible by 7, then the original number is divisible by 7.
Below are some of the examples that shows the application of this rule.
Example 1: 1234
1234 –> 123 – 8 = 115 –> 11 – 10 = 1.
1 is not divisible by 7. Hence, then number 1234 is not divisible by 7.
Example 2: 833
833 –> 83 – 6 = 77
77 is divisible by 7. Hence, the number 833 is divisible by 7.
Divisible by 13:
To check if a number is divisible by 13 just follow these simple steps:
- Multiply four times the last digit of the original number and add it to the truncated number.
- Apply step 1 over and over multiple times until you get a single digit or a double digit value.
- If the resultant value is divisible by 13, then the original number is divisible by 13.
Below are some of the examples that shows the application of this rule.
Example 1: 50674
50674 –> 5067 + 16 = 5083 –> 508 + 12 = 520 –> 52 + 0 = 52 –> 5 + 8 = 13
13 is divisible by 3. Hence, the number 50674 is divisible by 13.
Example 2: 4987
4987 –> 498 + 28 = 526 –> 52 + 24 = 76 –> 7 + 24 = 31 –> 3 + 4 = 7
7 is not divisible by 13. Hence, the number 4987 is not divisible by 13.
Divisible by 17:
To check if a number is divisible by 17 just follow these simple steps:
- Multiply five times the last digit of the original number and subtract it from the truncated number.
- Apply step 1 over and over multiple times until you get a single digit or a double digit value.
- If the resultant value is divisible by 17, then the original number is divisible by 17.
Example 1: 3961
3961 –> 396 – 5 = 391 –> 39 – 5 = 34
34 is divisible by 17. Hence, the number is divisible by 17.
Example 2: 45672
45672 –> 4567 – 10 = 4557 –> 455 – 35 = 420 –> 42 – 0 = 42
42 is not divisible by 17. Hence, 45672 is not divisible by 17.
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