There is a shortcut rule for the test of divisibility of 7.

A number can be divisible by 7 only if the difference of the number formed by the last three digis and the number formed by the rest of the digits is divisible by 7.

For example, is 137125 divisible by seven?

So, we take the difference as 137 - 125 = 84

Since the difference is divisible by 7, 137125 is also divisible by 7. (CHECK IT OUT)

Let us take another example: 12478375.

Solution: Step 1. 12478 - 375 = 12103

Step 2. 12 - 103 = -91

Since 91 is divisible by 7, 12478375 is also divisible by 7.

Let us make it simpler. We take 70000: 70 - 0 = 70 which is divisible by 7.

Three digit numbers are easy enough for u to divide by 7, hence, 3 digit no.s can be divided directly

Hope this Helps!

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There are 2 methods for the divisibility test of 7:-

Method No. 1:-

Take the last digit in a number.Double and subtract the last digit in your number from the rest of the digits. Repeat the process for larger numbers.

eg:-

364

double of the no. 4=8

36-8=28

As 28 is divisible by 7,364 is also a divisible of 7.

Method No. 2:-

- Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2,6, 4, 5. Repeat this sequence as necessaryAdd the products.If the sum is divisible by 7 - so is your number.

eg:-

364

(3*1) +(6*3)+(4*2)

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here it is...

If you double the last digit and subtract it from the rest of the number and the answer is:**0**, or**divisible by 7**
| 672 (Double 2 is 4, 67-4=63, and 63÷7=9) 905 (Double 5 is 10, 90-10=80, and 80÷7=11 |

hope it helps!!

cheers!!!

thumbs up plz...

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## Divisibility rules for numbers 1–20

Divisor | Divisibility condition | Examples |
---|---|---|

1 | Automatic. | Any integer is divisible by 1. |

2 | The last digit is even (0, 2, 4, 6, or 8).^{[1]}^{[2]} | 1,294: 4 is even. |

3 | Sum the digits.^{[1]}^{[3]}^{[4]} | 405 → 4 + 0 + 5 = 9 and 636 → 6 + 3 + 6 = 15 which both are clearly divisible by 3. 16,499,205,854,376 → 1+6+4+9+9+2+0+5+8+5+4+3+7+6 sums to 69 → 6 + 9 = 15 → 1 + 5 = 6, which is clearly divisible by 3. |

Subtract the quantity of the digits 2, 5 and 8 in the number from the quantity of the digits 1, 4 and 7 in the number. | Using the example above: 16,499,205,854,376 has four of the digits 1, 4 and 7; four of the digits 2, 5 and 8; ∴ Since 4 − 4 = 0 is a multiple of 3, the number 16,499,205,854,376 is divisible by 3. | |

4 | Examine the last two digits.^{[1]}^{[2]} | 40832: 32 is divisible by 4. |

If the tens digit is even, and the ones digit is 0, 4, or 8. If the tens digit is odd, and the ones digit is 2 or 6. | 40832: 3 is odd, and the last digit is 2. | |

Twice the tens digit, plus the ones digit. | 40832: 2 × 3 + 2 = 8, which is divisible by 4. | |

5 | The last digit is 0 or 5.^{[1]}^{[2]} | 495: the last digit is 5. |

6 | It is divisible by 2 and by 3.^{[5]} | 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6. |

7 | Form the alternating sum of blocks of three from right to left.^{[6]}^{[4]} | 1,369,851: 851 − 369 + 1 = 483 = 7 × 69 |

Subtract 2 times the last digit from the rest. (Works because 21 is divisible by 7.) | 483: 48 − (3 × 2) = 42 = 7 × 6. | |

Or, add 5 times the last digit to the rest. (Works because 49 is divisible by 7.) | 483: 48 + (3 × 5) = 63 = 7 × 9. | |

Or, add 3 times the first digit to the next. (This works because 10a + b − 7a = 3a + b − last number has the same remainder) | 483: 4×3 + 8 = 20 remainder 6, 6×3 + 3 = 21. | |

Multiply each digit (from right to left) by the digit in the corresponding position in this pattern (from left to right): 1, 3, 2, -1, -3, -2 (repeating for digits beyond the hundred-thousands place). Then sum the results. | 483595: (4 × (-2)) + (8 × (-3)) + (3 × (-1)) + (5 × 2) + (9 × 3) + (5 × 1) = 7. | |

8 | If the hundreds digit is even, examine the number formed by the last two digits. | 624: 24. |

If the hundreds digit is odd, examine the number obtained by the last two digits plus 4. | 352: 52 + 4 = 56. | |

Add the last digit to twice the rest. | 56: (5 × 2) + 6 = 16. | |

Examine the last three digits^{[1]}^{[2]} | 34152: Examine divisibility of just 152: 19 × 8 | |

Add four times the hundreds digit to twice the tens digit to the ones digit. | 34152: 4 × 1 + 5 × 2 + 2 = 16 | |

9 | Sum the digits.^{[1]}^{[3]}^{[4]} | 2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9. |

10 | The last digit is 0.^{[2]} | 130: the last digit is 0. |

11 | Form the alternating sum of the digits.^{[1]}^{[4]} | 918,082: 9 − 1 + 8 − 0 + 8 − 2 = 22. |

Add the digits in blocks of two from right to left.^{[1]} | 627: 6 + 27 = 33. | |

Subtract the last digit from the rest. | 627: 62 − 7 = 55. | |

If the number of digits is even, add the first and subtract the last digit from the rest. | 918,082: the number of digits is even (6) → 1808 + 9 − 2 = 1815: 81 + 1 − 5 = 77 = 7 × 11 | |

If the number of digits is odd, subtract the first and last digit from the rest. | 14,179: the number of digits is odd (5) → 417 − 1 − 9 = 407 = 37 × 11 | |

12 | It is divisible by 3 and by 4.^{[5]} | 324: it is divisible by 3 and by 4. |

Subtract the last digit from twice the rest. | 324: 32 × 2 − 4 = 60. | |

13 | Form the alternating sum of blocks of three from right to left.^{[6]} | 2,911,272: −2 + 911 − 272 = 637 |

Add 4 times the last digit to the rest. | 637: 63 + 7 × 4 = 91, 9 + 1 × 4 = 13. | |

Multiply each digit (from right to left) by the digit in the corresponding position in this pattern (from left to right): -3, -4, -1, 3, 4, 1 (repeating for digits beyond the hundred-thousands place). Then sum the results.^{[7]}. | 30,747,912: (2 × (-3)) + (1 × (-4)) + (9 × (-1)) + (7 × 3) + (4 × 4) + (7 × 1) + (0 × (-3)) + (3 × (-4)) = 13. | |

14 | It is divisible by 2 and by 7.^{[5]} | 224: it is divisible by 2 and by 7. |

Add the last two digits to twice the rest. The answer must be divisible by 14. | 364: 3 × 2 + 64 = 70. | |

15 | It is divisible by 3 and by 5.^{[5]} | 390: it is divisible by 3 and by 5. |

16 | If the thousands digit is even, examine the number formed by the last three digits. | 254,176: 176. |

If the thousands digit is odd, examine the number formed by the last three digits plus 8. | 3,408: 408 + 8 = 416. | |

Add the last two digits to four times the rest. | 176: 1 × 4 + 76 = 80. 1168: 11 × 4 + 68 = 112. | |

Examine the last four digits.^{[1]}^{[2]} | 157,648: 7,648 = 478 × 16. | |

17 | Subtract 5 times the last digit from the rest. | 221: 22 − 1 × 5 = 17. |

18 | It is divisible by 2 and by 9.^{[5]} | 342: it is divisible by 2 and by 9. |

19 | Add twice the last digit to the rest. | 437: 43 + 7 × 2 = 57. |

20 | It is divisible by 10, and the tens digit is even. | 360: is divisible by 10, and 6 is even. |

If the number formed by the last two digits is divisible by 20. | 480: 80 is divisible by 20. |

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