# Recent questions tagged factors

1 vote
1
Let $P= \{2,3,4,\ldots 100\}$ and $Q= \{101,102,103,\ldots 200\}.$ How many elements of $Q$ are there such that they do not have any element of $P$ as a factor? $20$ $24$ $23$ $21$
2
Find the smallest number $y$ such that $y \times 162$ $(y$ multiplied by $162)$ is a perfect cube. $A)24$ $B)27$ $C)32$ $D)36$
3
What is the smallest number, which when increased by 5 is completely divisible by 8, 11 and 24? 264 259 269 None of these
1 vote
4
For the product $n(n + 1)(2n + 1)$, $n \hat{I} N$, which one of the following is necessarily false? It is always even Divisible by $3$. Always divisible by the sum of the square of first n natural numbers Never divisible by $237$.
1 vote
$5^{4}-1$ is divisible by $13$ $31$ $5$ none of these
If n is any odd number greater than $1$, then the largest number that divides $n(n^{2} - 1)$ is: $48$ $24$ $6$ None of these