Telangana Board Solutions for Chapter: Real Numbers, Exercise 4: Exercise

Use Euclid's algorithm to find the $\mathrm{HCF}$ of $900$ and $270$.

Use Euclid's algorithm to find the $\mathrm{HCF}$ of $196$ and $38220$.

Use Euclid's algorithm to find the $\mathrm{HCF}$ of $1651$ and $2032$.

Use division algorithm to show that any positive odd integer is of the form $6q+1$, or $6q+3$ or $6q+5$, where $q$ is some integer.

Use division algorithm to show that the square of any positive integer is of the form $3p$ or $3p+1$.

Use division algorithm to show that the cube of any positive integer is of the form $9m, 9m+1$ or $9m+8$.

Show that one and only one out of $n, n+2$ or $n+4$ is divisible by $3$, where $n$ is any positive integer.