Test the divisibility of the following numbers by 7 :
(i) 826 (ii) 117 (iii) 2345 (iv) 6021 (v) 14126 (vi) 25368

Answer

To test the divisibility of the given numbers by 7, we will use the divisibility rule for 7. The rule states that we should double the last digit of the number, subtract it from the rest of the number (excluding the last digit), and check if the result is divisible by 7. Let's apply this rule step by step for each number.

### (i) 826
1. Last digit: **6**
2. Double the last digit: **6 × 2 = 12**
3. Rest of the number: **82**
4. Subtract: **82 - 12 = 70**
5. Check divisibility: **70 ÷ 7 = 10** (which is an integer)

**Conclusion:** 826 is divisible by 7.

### (ii) 117
1. Last digit: **7**
2. Double the last digit: **7 × 2 = 14**
3. Rest of the number: **11**
4. Subtract: **11 - 14 = -3**
5. Check divisibility: **-3 is not divisible by 7** (since 7 is larger than -3)

**Conclusion:** 117 is not divisible by 7.

### (iii) 2345
1. Last digit: **5**
2. Double the last digit: **5 × 2 = 10**
3. Rest of the number: **234**
4. Subtract: **234 - 10 = 224**
5. Check divisibility: **224 ÷ 7 = 32** (which is an integer)

**Conclusion:** 2345 is divisible by 7.

### (iv) 6021
1. Last digit: **1**
2. Double the last digit: **1 × 2 = 2**
3. Rest of the number: **602**
4. Subtract: **602 - 2 = 600**
5. Check divisibility: **600 ÷ 7 ≈ 85.71** (not an integer)

**Conclusion:** 6021 is not divisible by 7.

### (v) 14126
1. Last digit: **6**
2. Double the last digit: **6 × 2 = 12**
3. Rest of the number: **1412**
4. Subtract: **1412 - 12 = 1400**
5. Check divisibility: **1400 ÷ 7 = 200** (which is an integer)

**Conclusion:** 14126 is divisible by 7.

### (vi) 25368
1. Last digit: **8**
2. Double the last digit: **8 × 2 = 16**
3. Rest of the number: **2536**
4. Subtract: **2536 - 16 = 2520**
5. Check divisibility: **2520 ÷ 7 = 360** (which is an integer)

**Conclusion:** 25368 is divisible by 7.

### Summary of Results:
- 826: Divisible by 7
- 117: Not divisible by 7
- 2345: Divisible by 7
- 6021: Not divisible by 7
- 14126: Divisible by 7
- 25368: Divisible by 7