The Fundamental Theorem of Arithmetic

The product of two consecutive prime numbers is $3127$. What is the greater number?

Show that the number of the form $7^n$, $n$ is natural number cannot have unit digit zero.

Find the numbers by which $7289$ will be divisible.

For _____ values of $x$, $2^x\times 5^x$ ends in $5$. 

Find the simplest form of $\frac{92}{115}$.

If $p^2$ is an even integer, then $p$ must be an even integer.

Describe, why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers?

Sum of powers of prime factors of $196$ is:

Express number $20570$ as product of prime factors.

Express the number $3825$ as product of prime factors.

Express the number $140$ as a product of prime factors.

Express number $945$ as a product of its prime factors.

Express number $468$ as product of its prime factors.

If two numbers are written in the form $m= p{q}^3$ and $n= p^3{q}^2$ then, HCF of $m, n$ where $p, q$ are prime numbers is

Determine the prime factorization of each of the following positive integer:                                 [2 Marks each]

$\left(\mathrm{i}\right)$ $20570$

$\left(\mathrm{ii}\right)$ $58500$

$\left(\mathrm{iii}\right)$ $45470971$  

$7\times 5\times 3\times 1$ is a prime number.