Using rules of divisibility find whether the numbers 62530 and 28786 are divisible by 37, given that 37 exactly divides the numbers 45658 and 16872

Answer

To determine whether the numbers 62530 and 28786 are divisible by 37, we can use the rule of divisibility for 37. This rule states that we can take the last digit of the number, multiply it by 3, and subtract that from the remaining number. If the result is divisible by 37, then the original number is also divisible by 37.

### Step-by-Step Solution:

**Step 1: Check divisibility of 62530**
1. Identify the last digit of 62530, which is 0.
2. Multiply the last digit (0) by 3:
\[ 0 \times 3 = 0 \]
3. Remove the last digit from the original number to get the remaining number:
\[ 6253 \]
4. Subtract the result from the remaining number:
\[ 6253 - 0 = 6253 \]
5. Now, we need to check if 6253 is divisible by 37.
\[ 6253 \div 37 = 169 \]
Since 169 is a whole number, 6253 is divisible by 37.

**Conclusion for 62530:**
Since 6253 is divisible by 37, it follows that 62530 is also divisible by 37.

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**Step 2: Check divisibility of 28786**
1. Identify the last digit of 28786, which is 6.
2. Multiply the last digit (6) by 3:
\[ 6 \times 3 = 18 \]
3. Remove the last digit from the original number to get the remaining number:
\[ 2878 \]
4. Subtract the result from the remaining number:
\[ 2878 - 18 = 2860 \]
5. Now, we need to check if 2860 is divisible by 37.
\[ 2860 \div 37 = 77.57 \]
Since 77.57 is not a whole number, 2860 is not divisible by 37.

**Conclusion for 28786:**
Since 2860 is not divisible by 37, it follows that 28786 is also not divisible by 37.

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### Final Results:
- 62530 is divisible by 37.
- 28786 is not divisible by 37.