Question

find the greatest number which divides 131, 160 and 223 leaving remainders 7,5,and 6,respectively​

Answer 1

Since the divisor should leave 7,5,6 as remainders after dividing 131,160 and  223.

So 124 , 155 and 217 should be divisible by this unknown number.

Let’s do prime factorization of 124, 155, 217 to find the largest number

Prime factors of 124  = 2^2 . 31

Prime factors of 155  = 5 . 31

Prime factors of 217  = 7 . 31

∴ HCF(124,155,217) = 31

Required number = 31

Hope  this helps!