QQuestionMathematics
QuestionMathematics
160 is divisible by which of the following numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10?
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Answer
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Step 1:I'll solve this step by step, checking divisibility for each number:
Step 2:: Divisibility by 2
- $$160 \div 2 = 80$$ (whole number)
- A number is divisible by 2 if it's even - 160 is divisible by 2 ✓
Step 3:: Divisibility by 3
- Sum of digits: $$1 + 6 + 0 = 7
- 7 \div 3 = 2 \text{ remainder } 1 - 160 is NOT divisible by 3 ✗
Step 4:: Divisibility by 4
- Check last two digits: $$60 \div 4 = 15$$ (whole number)
- 160 is divisible by 4 ✓
Step 5:: Divisibility by 5
- $$160 \div 5 = 32$$ (whole number)
- Ends in 0 - 160 is divisible by 5 ✓
Step 6:: Divisibility by 6
- Must be divisible by 2 AND 3 - Divisible by 2 ✓, but NOT by 3 - 160 is NOT divisible by 6 ✗
Step 7:: Divisibility by 7
- $$160 \div 7 = 22 \text{ remainder } 6
- 160 is NOT divisible by 7 ✗
Step 8:: Divisibility by 8
- Check last three digits: $$160 \div 8 = 20$$ (whole number)
- 160 is divisible by 8 ✓
Step 9:: Divisibility by 9
- Sum of digits: $$1 + 6 + 0 = 7
- 7 \div 9 = 0 \text{ remainder } 7 - 160 is NOT divisible by 9 ✗
Step 10:: Divisibility by 10
- $$160 \div 10 = 16$$ (whole number)
- Ends in 0 - 160 is divisible by 10 ✓
Final Answer
160 is divisible by 2, 4, 5, 8, and 10.
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