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Homework: Prime Factors
1. A two-digit prime number is randomly selected. What is the probability that
its digits sum to 9?
2. Twin primes are prime pairs that differ by 2. What is the sum of the largest pair
of twin primes less than 50?
3. What is the smallest positive four-digit number that gives a quotient of 432 with
remainder 2 when divided by a positive one-digit number?
4. What is the greatest prime divisor of the sum
?
5. How many positive integers less than 101 are multiples of either 5 or 7, but not
both at the same time?
6. If the product of any two numbers of
are divisible by the third, what is
the smallest possible value of X?
7. Find the product of the positive divisors of
8. For how many values of
is
that are multiples of 12.
the lcm of
and ?
9. How many positive integers have exactly 3 proper divisors (divisors that are not
the number itself), each of which is less than 50?
10. Compute the sum of the divisors of the smallest positive integer with six
positive odd integer divisors and twelve positive even integer divisors.