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160 is divisible by which of the following numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10? Show all work.
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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.