The prime factorization of $30$ can be written as: $(A)$ $5 \times 6$,$(B)$ $10 \times 3$,$(C)$ $2 \times 3 \times 5$,$(D)$ $1 \times 30$

Find the $HCF$ and $LCM$ of the following pair of integers $510$ and $92$ and verify that $HCF \times LCM = \text{product of the two numbers}$.

The difference between the $HCF$ and $LCM$ of two prime numbers $7$ and $11$ is . . . . . . .

If a positive integer is of the form $3q + 1$,where $q$ is a natural number,then its square can be written in the form $3m + 1$. Is the statement true or false?

Find the $HCF$ of $12$,$15$,and $21$.

Every composite number greater than $1$ can be expressed (factorized) as a product of primes,and this factorization is . . . . . . apart from the order in which the prime factors occur. ($0$,$1$,unique)