Question

14)The number 673 and 865 is divisible by which of the following leaving a remainder 1

Answer 1

Answer:

582146

Step-by-step explanation:

lcm(673, 865) + 1=582146

Answer 2

We have to find the largest number which divides 673 and 865 leaving remainder 1 in each case.

Let largest number is x.

in order to make 673 and 865 completely divisible by x, we need to deduce the remainder 1 from both the cases.

i.e., 673 - 1 = 672 , 865 - 1 = 864

now find HCF of 672 and 864.

prime factors of 672 = 2 × 2 × 2 × 2 × 2 × 3 × 7

prime factors of 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

so, highest common factors of 672 and 864 = 2 × 2 × 2 × 2 × 2 × 3 = 96

hence, HCF{672, 864} = 96

therefore, largest number is 96.