Without carrying out actual division, find if 293944 is divisible by 56 or not

Answer

To determine if 293944 is divisible by 56 without performing actual division, we can use the rules of divisibility for 7 and 8, since 56 is the product of these two numbers. We will follow these steps:

### Step 1: Check divisibility by 7
1. **Identify the last digit**: The last digit of 293944 is 4.
2. **Double the last digit**: Double 4 to get 8.
3. **Subtract from the rest of the number**: Subtract 8 from the remaining number (29394):
\[ 29394 - 8 = 29386 \]
4. **Check if 29386 is divisible by 7**:
- Divide 29386 by 7:
- 7 goes into 29 four times (28), remainder 1.
- Bring down the next digit (3), making it 13. 7 goes into 13 once (7), remainder 6.
- Bring down the next digit (8), making it 68. 7 goes into 68 nine times (63), remainder 5.
- Bring down the next digit (6), making it 56. 7 goes into 56 exactly eight times (56), remainder 0.
- Since the remainder is 0, 29386 is divisible by 7.

### Step 2: Check divisibility by 8
1. **Identify the last two digits**: The last two digits of 293944 are 44.
2. **Check if 44 is divisible by 8**:
- Divide 44 by 8:
- 8 goes into 44 five times (40), remainder 4.
- Since the remainder is not 0, 44 is not divisible by 8.

### Step 3: Check divisibility by 2
1. **Check if the number is even**: Since 293944 ends with a 4, it is even.
- Therefore, 293944 is divisible by 2.

### Conclusion
Since 293944 is divisible by 7 and 2, but **not divisible by 8**, we conclude that **293944 is not divisible by 56**.

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