Question

The H.C.F. of 608 and 544; 638 and 783; 425 and 476 respectively are?
A. 32, 29, 17
B. 18, 32, 29
C. 29, 35, 15
D. 32, 20, 24

Answer 1

Hint: To find the highest common factor, one needs to identify all the numbers which can be factors of the numbers in question and then find which of them are common and multiply them to get the highest factor.

Complete step by step solution:
Our first H.C.F. will be between 608 and 544. My tip here is to start the H.C.F. and keep in mind to find the common factors in each step from the numbers between 1-7. If it is no longer possible, only then to move to higher numbers and break each of them into its factors.
The division for H.C.F. is done in such a fashion that on the left side are the divisors and below are the quotients of the division for all the numbers whose H.C.F. is being found out together as shown below. Since all the divisors are factors only so there is no chance of having remainders.

And so, the H.C.F. of 608 and 544 is $2 \times 2 \times 2 \times 2 \times 2 = 32$
Now we will work with 638 and 783. When using this flow chart method, you will observe that they don’t have any common factor between 1 and 7 and so we break them into multiples.
$\
  638 = 1 \times 2 \times 11 \times 29 \\
  783 = 1 \times 27 \times 29 \\
\ $
We see that only common factors are 1 and 29. Thus $H.C.F. = 1 \times 29 = 29$.
Similarly, when working with 425 and 476, you will observe that they don’t have any common factor between 1 and 7 and so we break them into multiples too.
$\
  425 = 1 \times 5 \times 5 \times 17 \\
  476 = 1 \times 2 \times 2 \times 7 \times 17 \\
\ $

In this case, only common factors are 1 and 17. Thus $H.C.F. = 1 \times 17 = 17$.

Note:
In such multiple type questions with more than one subpart, always start from the part which has different solutions in each of the options and get its answer. That one answer will eliminate the other options directly, eliminating all other options, thereby saving time.