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Apply integers across unfamiliar problems: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Separate divisibility, remainders and prime-factor restrictions before calculating. Test whether zero, negative integers or endpoints belong to the allowed set.
How many integers from -12 through 17, inclusive, are multiples of 4?
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An integer leaves remainder 5 when divided by 8. What remainder does three times that integer leave when divided by 8?
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What is the smallest positive integer that must multiply 540 to make a perfect square?
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How many positive divisors of 180 are odd?
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What is the units digit of 7 raised to the 23rd power?
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A two-digit positive integer has digit sum 12 and is divisible by 4. What is the largest such integer?
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How many integers strictly between 20 and 70 are divisible by 6 but not by 9?
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What is the smallest positive integer leaving remainder 1 when divided by both 6 and 8 and divisible by 5?
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The greatest common divisor of positive integers a and b is 6 and their least common multiple is 90. What is ab?
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How many positive integers less than 50 have exactly three positive divisors?
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What is the greatest integer k such that 12 to the power k divides 18 factorial?
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For a counting error, list a small representative set and identify what was omitted or counted twice; for a divisibility error, rewrite the prime factors.