Three positive integers a, b and c have, in pairs, highest common factors (a, b) = 24, (b, c) = 198 and (a, c) = 210. (a) What is the highest common factor of a, b and c? (b) Find the smallest values of a, b and c which satisfy the given criteria.

HCF(a,b,c)=6

Smallest values of a, b and c are 840, 792 and 6930 respectively.

Step-by-step explanation:

It is given that,

HCF(a,b)=24, HCF(b,c)=198 and HCF(a,c)=210.

If means 24 and 210 are the factors of a.

If means 24 and 198 are the factors of b.

If means 198 and 210 are the factors of c.

Therefore, the smallest values of a, b and c which satisfy the given criteria are 840, 792 and 6930 respectively.

Now,

Therefore, HCF of a, b and c is 6.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

can you complete your sentence? i could !