MEDIUM
Earn 100

Express each number as the product of its prime factors. Use repeated division method.

117

Important Questions on Number Theory

HARD
Let N denote the number of all natural numbers n such that n is divisible by a prime p>n and p<20. What is the value of N?
EASY
There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The last number is :
MEDIUM
Consider the set E={5,6,7,8,9}. For any partition {A,B} of E, with both A and B non-empty, consider the number obtained by adding the product of elements of A to the product of elements of B. Let N be the largest prime number among these numbers. Find the sum of the digits of N.
HARD
The prime numbers a, b and c are such that a+b2=4c2. Determine the sum of all possible values of a+b+c.
HARD
Suppose a,b,c are positive integers such that 2a+4b+8c=328. Then a+2b+3cabc is equal to-
EASY
If a and b are positive integers such that a2-b2 is a prime number, then a2-b2 is equal to:
EASY
Find the smallest positive integer n10 such that n+6 is a prime and 9n+7 is a perfect square.
EASY
A prime number p is called special if there exist primes p1, p2, p3, p4 such that p=p1+p2=p3-p4.
The number of special primes is
 
MEDIUM
For an integer n, let Sn=n+1,n+2,., n+18. Which of the following is true for all n10 ?
EASY
A two-digit number ab¯ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits a & b. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is
MEDIUM
The number of digits in the decimal expansion of 165516 is
HARD
The number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes is
EASY
What is the sum of exponents of prime factors in the prime factorization of 98?
EASY

If the following expression can be written as 9ymzn, find the value of (m-n).

9×y×y×y×y×z×z×z

EASY

If the exponential form of a×a×a×b×b×b×b×c×c×c=axbycz, then find the value of x+y+z

MEDIUM
If 63.9805=6A+3B+9C+8D+5E, then what is the value of 4A+7B+6C+D+3E?
MEDIUM

Write the following in exponential form.

m×m×m×m×m

MEDIUM
The number 2.35×104 in the usual form is written as
MEDIUM
23+23+23+23 is equal to _____