Tamil Nadu Board Solutions for Chapter: Numbers And Sequences, Exercise 8: Exercise 2.2

If $m, n$ are natural numbers, for what values of $m$, does $2^n\times 5^m$ ends in $5$?

Find the $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of $252525$ and $363636$.

If $13824=2^a\times 3^b$, then find $a$ and $b$.

If $p_1^{x_1}\times p_2^{x_2}\times p_3^{x_3}\times p_4^{x_4}=113400$, where $p_1, p_2, p_3, p_4$ are primes in ascending order and $x_1, x_2, x_3, x_4$ are integers, find the value of $p_1, p_2, p_3, p_4$ and $x_1, x_2, x_3, x_4$.

Find the $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ and $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of $408$ and $170$ by applying the fundamental theorem of arithmetic.

Find the greatest number consisting of $6$ digits which is exactly divisible by $24, 15, 36$?

What is the smallest number that when divided by three numbers such as $35, 56$ and $91$ leaves remainder $7$ in each case?

Find the least number that is divisible by the first ten natural numbers.