Question

The largest number which divides 70 and 125 leaving remainders 55 & 8, respectively. (a) 13 (b) 65 (c) 875 (d) 1750​

Answer 1

Step-by-step explanation:

Since it is given that we have to find the largest number that divides 70 and 125 each, it means that we need to find the highest common factor, i.e. HCF. That leaves 5 and 8 as the remainder respectively.

By prime-factorization method;

The prime factors of 65 are: 65=5×13

And the prime factors of 117 are: 117=3×3×13

Hence, the common prime factor of 65 and 117 is 13.

Now, dividing 70 by 13 we get 5 as remainder

13⎞⎠⎟706505¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯5

Similarly, dividing 125 by 13 we get 8 as remainder

13⎞⎠⎟125117008¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯9

Therefore, 13 is the largest number that divides 70 and 125 and leaves 5 and 8 as the remainder respectively.

So, the correct answer is “Option A”.

Answer 2

Answer:

3

Step-by-step explanation:

70-55=15

125-8=117

HCF of 15 and 117 is

15=3×5

117=3×3×15

Hence, 3 is the largest number which divides 70 and 125 leaving remainders 55 and 8