Factor, Common Factor and Highest Common Factor

Three different containers contain different quantities of a mixture of milk and water, whose measurements are $403 \mathrm{kg}, 434 \mathrm{kg}$ and $465 \mathrm{kg}$. What biggest measure be there to measure all the different quantities exactly?

Find H.C.F. Three number are in the ratio of $3 : 4 : 5$ and their L.C.M. is $2400$ ?

The product of two numbers is $2160$ and their HCF is $12$. If the sum of the squares of the two numbers is $4896$, then what is the mean of the two numbers?

What is the HCF of $3^{29}-9$ and $3^{38}-9$?

Find all pairs of positive integers whose sum is $91$ and H.C.F is $13$. Show your work.

The HCF of $k$ and $93$ is $31$, where $k$ is a natural number. Which of these can be true for some values of $k$?

$\left(\mathrm{i}\right)$ $k$ is a multiple of $31$

$\left(\mathrm{ii}\right)$$k$ is a multiple of $93$

$\left(\mathrm{iii}\right)$ $k$ is an even number.

$\left(\mathrm{iv}\right)$ $k$ is an odd number.

Find the smallest pair of $4$ - digit numbers such that the difference between them is $303$ and their HCF is $101$. Show your steps

Find the GCD  of $7x^2 \text{and} 21x$

If $\left(\mathrm{x}+\mathrm{k}\right)$ is the HCF of ${\mathrm{x}}^2+\mathrm{px}+\mathrm{q}$ and  ${\mathrm{x}}^2+\mathrm{qx}+\mathrm{p}$ where $\mathrm{p}\ne \mathrm{q}$then what is the value of $\mathrm{k}$?

The greatest number, which when divide $989$ and $1327$ leave remainders $5$ and $7$ respectively, is:

The maximum number of students among whom $1001$ pens and $910$ pencils can be distributed in such a way that each student gets same number of pens and same number of pencils, is:

Three numbers are in the ratio $1:2:3$ and their HCF is $12$ . The numbers are_____.

Find the greatest number which will divide $148,246$ and $623$ leaving remainders $4,6$ and $11$ , respectively:

The LCM of two numbers is $36$ times that of their HCF. The product of the numbers is $3600$. Find their HCF:

The LCM of three numbers is $4752$ and HCF is $6$. If the two numbers are $48$ and $66$, the third number is______.

Find the HCF of $2378$ and $3280:$

Find the greatest number which will exactly divide $200$ and $320$.

Find the HCF of the following

$3,12$

_____

Find the common factor of $20$ and $36$.

Find the common factor of $35$ and $50$.