By Euclid's division lemma, a positive integer a can be written as a = 3b + 5, where 5 is the remainder (so 5 < b). If a = 23, find b.
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Explanation: By Euclid's division lemma, $23 = 3b + 5$ with remainder $5$, so $3b = 18$ and $b = 6$. The remainder condition $5 < b$ holds since $5 < 6$, and indeed $23 = 6 \times 3 + 5$.
Question 2 of 6medium
Find the least number that must be added to 302 to make it divisible by 17 using Euclid's lemma.
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Explanation: $302 = 17 \times 17 + 13$, so the remainder is $13$. To make it divisible by $17$, add $17 - 13 = 4$. Check: $302 + 4 = 306 = 17 \times 18$.
Question 3 of 6medium
How many distinct prime factors does the number \(2^{8} \times 3^{5} \times 5^{2} \times 7\) have?
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18
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Explanation: Distinct prime factors are 2, 3, 5, 7 → only 4 distinct primes. Exponents don't change distinct count
Question 4 of 6medium
If x = 0.142857142857… and y = 0.285714285714…, what is x + y?
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