Factors of a Number

Q. The number of ways in which $5^7$ can be expressed as a product of three factors:

1. 7
2. 8
3. 9
4. none of these

Q. Two friends Harry and Jayesh were discussing about two numbers. They found the two numbers to be such that one was twice the other. However, both had the same number of prime factors, while the larger one had 4 more factors than the smaller one. What are the numbers?

1. 40, 80
2. 20, 40
3. 30, 60
4. 50, 100

Q. n is a number, such that 2n has 28 factors and 3n has 30 factors. 6n has

1. 32
2. 28
3. 35
4. None of these

Q. A is a set of first 10 natural numbers. B is a subset of A such that B consists of exactly 2 numbers, both co-primes to each other. Find the maximum number of such possible subsets.

1. 29
2. 28
3. 31
4. 33

Q. If m + n = mn - 5, then the maximum number of ordered pairs of (m, n) for every m, n is a natural number.

1. 5
2. 6
3. 4
4. None of these

Q. How many pairs of positive integers m, n satisfy:
$\frac{1}{m}+\frac{4}{n}=\frac{1}{12},$ where n is an odd integer less than 60?

1. 5
2. 3
3. 6
4. 4

Q. The number of numbers less than or equal to 666 which are the products of exactly 4 distinct positive prime numbers is:

1. 7
2. can't be determined
3. 4
4. 8

Q. Number of divisors of the form 4n + 2; n $\ge$ 0 which can divide 240 is:

1. 8
2. 10
3. 3
4. 4

Q. A leading chocolate producing company produces 'abc' chocolates per hour (abc is a three digit positive number). In how many hours it will produce `abcabc' chocolates?

1. abc
2. 101
3. 1001
4. can't be determined

Q. $N=2^3\times 5^3$. How many sets of two distinct factors of N are co-prime to each other?

1. 12
2. 24
3. 23
4. 11