Question

the largest number which divides 70 and 125 leaving remainder 5 and 8 ​

Answer 1

Answer:

first subtract the given numbers

70-5=65

125-8=117

then find HCF,

65=5*13

117=3*3*13

    =3²*13

HCF=13

Answer 2

Since 5 and 8 are the remainders of 70 and 123,respectively.Thus,after subtracting these remainders from the numbers, we have the numbers 65 and 117.

Now required number = HCF of 65 and 117

For this ,  117 = 65×1+52 [∵ dividend = divisor×quotient + remainder]

→     65 = 52×1+13

→     52 = 13×4+0

HCF = 13

Hence 13 is the largest number which divides 70 and 125,leaving remainder 5 and 8.