Prime Time

The sum of all factors of $6$ is:

If a number is divisible by $9$, it must be divisible by:

How many factors does the number $11$ have?

Which of these is the first common multiple of $5$ and $7$?

The length, breadth, and height of a room are $825\text{ cm}$, $675\text{ cm}$, and $450\text{ cm}$ respectively. Determine the length of the longest tape that can measure all three dimensions of the room exactly.

Find the smallest number which is exactly divisible by $8, 12,$ and $16$.

What is the HCF of $15, 30,$ and $45$?

What is the value of $(HCF \times LCM)$ for two numbers $a$ and $b$?

Find the greatest number of 4 digits exactly divisible by $12, 15, 18, 27$.

Find the smallest number which when divided by $6, 15$, and $18$ leaves a remainder of $5$ in each case.

What is the product of the first three prime numbers ($2, 3, 5$)?

Is $2$ the only even prime number?

Which prime number is between $40$ and $45$?

What is the sum of the smallest prime and the smallest composite number?

How many prime numbers are there in the range from $70$ to $90$?

Find the product of the prime numbers that are greater than $10$ but less than $15$.

The number $13$ is prime. If its digits are reversed, we get $31$, which is also prime. What is the difference between these two prime numbers?

How many prime numbers less than $50$ have the digit $3$ in the units place?

What is the largest prime number less than $200$?

Which prime number is both the sum and the difference of two prime numbers?

Which of these pairs of composite numbers is co-prime?

What is the HCF of $40$ and $41$?

Are $3$ and $5$ co-prime numbers?

Which pair is NOT co-prime for safekeeping a treasure?

Are $12$ and $17$ co-prime numbers?

Which of the following is the $HCF$ of the co-prime pair $(2, 3)$?

Find the $HCF$ of the numbers $4$ and $9$ for a treasure box lock.

Two numbers are co-prime. If one of them is $1$, what is their HCF?

How many pairs of co-prime numbers can be formed using the numbers $\{2, 3, 4, 5\}$?

Given that $HCF(a, b) = 1$, find $HCF(a-b, a+b)$ if $a=5$ and $b=3$.

Find the prime factorisation of $99$.

Find the prime factorisation of $98$.

Find the prime factorisation of $91$.

Find the prime factorisation of $88$.

Find the prime factorisation of 10000.

What is the sum of the prime factors of 30?

Which of the following numbers has the prime factorisation $2 \times 3 \times 5 \times 7$?

Which of the following is the prime factorisation of $231$?

What are the distinct prime factors of the number $102$?

Find the prime factorisation of $900$.

Is $100$ divisible by $4$?

Which of these numbers is divisible by $3$?

Is $25$ divisible by $5$?

Is $1,008$ divisible by $9$?

Find the digit $k$ such that the three-digit number $k44$ is divisible by $6$ and the two-digit number $2k$ is divisible by $4$.

If $x$ is a digit such that $58x$ is divisible by $4$, how many possible values can $x$ take?

What is the smallest number to be subtracted from $52$ to make it divisible by $11$?

If $x4y$ is a three-digit number divisible by $9$, where $x$ and $y$ are non-zero digits, what is the value of $x + y$?

What is the smallest number that should be added to $7777$ to make it divisible by $8$?

A number is divisible by $15$ but not by $2$. Which digit can never be in its units place?

Which number is a factor of $24$ but not a factor of $16$?

Every number is a multiple of:

What is the LCM of $8$ and $12$?

What is the HCF of $7$ and $11$?

What is the smallest $5$-digit number that is exactly divisible by $20$, $25$, and $30$?

Three bells toll at intervals of $12$, $15$, and $18$ minutes respectively. If they all toll together at $8:00$ AM, at what time will they next toll together?

Find the greatest number that will divide $37$, $50$, and $63$ leaving remainders $1$, $2$, and $3$ respectively.

How many factors does the number $360$ have?

Find the smallest $4$-digit number such that when it is divided by $12, 18, 21$ and $28$, it leaves a remainder $3$ in each case.

What is the sum of the digits of the smallest number which is divisible by both $15$ and $25$?