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Is {1,2,4,16,64} = {x: x is a factor of ...

Is {1,2,4,16,64} = {x: x is a factor of 32} ? Give reason.

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To determine if the set {1, 2, 4, 16, 64} is equal to the set {x: x is a factor of 32}, we need to find the factors of 32 and compare them to the elements in the first set. ### Step-by-Step Solution: 1. **Identify the factors of 32**: - A factor of a number is any number that divides that number without leaving a remainder. - We start with the number 32 and find its factors by dividing it by integers starting from 1. 2. **Finding the factors**: - 32 ÷ 1 = 32 (1 is a factor) - 32 ÷ 2 = 16 (2 is a factor) - 32 ÷ 4 = 8 (4 is a factor) - 32 ÷ 8 = 4 (8 is a factor) - 32 ÷ 16 = 2 (16 is a factor) - 32 ÷ 32 = 1 (32 is a factor) - Thus, the complete list of factors of 32 is {1, 2, 4, 8, 16, 32}. 3. **Compare the sets**: - The set of factors of 32 is {1, 2, 4, 8, 16, 32}. - The given set is {1, 2, 4, 16, 64}. - Now we compare the two sets. 4. **Check for equality**: - The elements in the first set are 1, 2, 4, 16, and 64. - The elements in the second set (factors of 32) are 1, 2, 4, 8, 16, and 32. - Notice that 64 is not a factor of 32, and 8 and 32 are missing from the first set. 5. **Conclusion**: - Since the two sets do not contain the same elements (64 is not a factor of 32), we conclude that {1, 2, 4, 16, 64} is not equal to {x: x is a factor of 32}. ### Final Answer: No, {1, 2, 4, 16, 64} is not equal to {x: x is a factor of 32} because 64 is not a factor of 32.
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