Test the divisibtlity of the following numbers by 8 :
(i) 9364 (ii) 2138 (iii) 36792 (iv) 901674 (v) 136976 (vi) 1790184

Answer

To determine if the given numbers are divisible by 8, we will follow the rule that states: **A number is divisible by 8 if the last three digits of that number are divisible by 8.**

Let's analyze each number step by step:

### Step 1: Check the number 9364
- **Last three digits:** 364
- **Divide 364 by 8:**
- 8 goes into 36 four times (8 x 4 = 32).
- Subtract 32 from 36 to get a remainder of 4.
- Bring down the next digit (4) to make it 44.
- 8 goes into 44 five times (8 x 5 = 40).
- Subtract 40 from 44 to get a remainder of 4.
- **Conclusion:** Since there is a remainder, **9364 is not divisible by 8.**

### Step 2: Check the number 2138
- **Last three digits:** 138
- **Divide 138 by 8:**
- 8 goes into 13 once (8 x 1 = 8).
- Subtract 8 from 13 to get a remainder of 5.
- Bring down the next digit (8) to make it 58.
- 8 goes into 58 seven times (8 x 7 = 56).
- Subtract 56 from 58 to get a remainder of 2.
- **Conclusion:** Since there is a remainder, **2138 is not divisible by 8.**

### Step 3: Check the number 36792
- **Last three digits:** 792
- **Divide 792 by 8:**
- 8 goes into 79 nine times (8 x 9 = 72).
- Subtract 72 from 79 to get a remainder of 7.
- Bring down the next digit (2) to make it 72.
- 8 goes into 72 nine times (8 x 9 = 72).
- Subtract 72 from 72 to get a remainder of 0.
- **Conclusion:** Since there is no remainder, **36792 is divisible by 8.**

### Step 4: Check the number 901674
- **Last three digits:** 674
- **Divide 674 by 8:**
- 8 goes into 67 eight times (8 x 8 = 64).
- Subtract 64 from 67 to get a remainder of 3.
- Bring down the next digit (4) to make it 34.
- 8 goes into 34 four times (8 x 4 = 32).
- Subtract 32 from 34 to get a remainder of 2.
- **Conclusion:** Since there is a remainder, **901674 is not divisible by 8.**

### Step 5: Check the number 136976
- **Last three digits:** 976
- **Divide 976 by 8:**
- 8 goes into 97 twelve times (8 x 12 = 96).
- Subtract 96 from 97 to get a remainder of 1.
- Bring down the next digit (6) to make it 16.
- 8 goes into 16 two times (8 x 2 = 16).
- Subtract 16 from 16 to get a remainder of 0.
- **Conclusion:** Since there is no remainder, **136976 is divisible by 8.**

### Step 6: Check the number 1790184
- **Last three digits:** 184
- **Divide 184 by 8:**
- 8 goes into 18 two times (8 x 2 = 16).
- Subtract 16 from 18 to get a remainder of 2.
- Bring down the next digit (4) to make it 24.
- 8 goes into 24 three times (8 x 3 = 24).
- Subtract 24 from 24 to get a remainder of 0.
- **Conclusion:** Since there is no remainder, **1790184 is divisible by 8.**

### Summary of Results:
- 9364: Not divisible by 8
- 2138: Not divisible by 8
- 36792: Divisible by 8
- 901674: Not divisible by 8
- 136976: Divisible by 8
- 1790184: Divisible by 8