Factor and multiple

Define: (1) factor (2) multiple Give four examples of each.

Every counting number has an infinite number of (a)factors (b) multiples prime factors (d) none of these

Write a proper fraction with denominator a multiple of 5 and numerator a multiple of 6.

Write a proper fraction with denominator a multiple of 3 and numerator a multiple of 4.

Write two rational numbers with denominator a multiple of 3 and numerator a multiple of 4, such that the denominator is less than the numerator.

Two dice are rolled simultaneously. Find the probability of : getting a multiple of 2 on one dice and a multiple of 3 on the other dice.

If s is a multiple of 12 and t is a multiple of 12, is 7s+5t a multiple of 12?

If A^(**)B us the greatest common factor of A and B, A$B is defined as the least common multiple of A and B, and AnnB is defined as equal to (A^(**)B) $ (A $ B) , then what is the value of 12nn15 ?

Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd integer greater than 3, but not a multiple of 3.