The teacher asked if 14560 is divisible by all of 2, 4, 5, 8 and 10. Guna checked for divisibility of 14560 by only two of these numbers and then declared that it was also divisible by all of them. What could those two numbers be?
The two numbers could be 8 and 5 (or 8 and 10).
Reasoning: If a number is divisible by 8, it is automatically divisible by 2 and 4. If a number is divisible by 5 and is even, it is divisible by 10. ∴ Checking divisibility by 8 and 5 (or 8 and 10) covers all cases.
Explanation
The divisibility rules create a hierarchy: If divisible by 8, then divisible by 4 and 2. If divisible by 5 and even, then divisible by 10. So checking divisibility by 8 and 5 (or 8 and 10) is sufficient to determine divisibility by all five numbers.
Solution Steps
Step 1: If a number is divisible by 8, it is automatically divisible by 4 and 2.
Step 2: If a number is divisible by 5 and is even, it is divisible by 10.
Step 3: So checking divisibility by 8 and 5 (or 8 and 10) covers all cases.
Step 4: 14560: Last three digits 560. 560 ÷ 8 = 70. Divisible by 8.
Step 5: 14560 ends in 0, so divisible by 5 and 10.
Step 6: Since divisible by 8, also divisible by 4 and 2.