Question

A number, which was to be divided by 105 (3 × 5 × 7) was
divided by 3, 5 and 7 in succession and the remainders were 2, 4 and 6 respectively. What would be the remainder when it is divided by 105?​

Answer 1

Answer:

104

Step-by-step explanation:

let no is x,

so,

x=3m+2

x=5n+4

x=7p+6

so simply

when x divide by 105 it give 104 remainder

hope it helps you

Answer 2

Hence, N when divided by 105 leaves the remainder as 104.

Given:

A number divided by 3, 5 and 7 in succession, remainders are 2, 4, 6.

To find: Remainder after division after 105

Solution:

Let the number be N

We know that,

N = 3p + 2 [1]

p = 5q + 4 [2]

q = 7r + 6 [3]

Putting [3] in [2], we get

p = 5(7r + 6) + 4

Putting this value of p in [1], we get

N = 3[5(7r + 6) + 4] + 2

⇒ N = 3(35r + 30 + 4) + 2

⇒ N = 105r + 90 + 12 + 2

⇒ N = 105r + 104

Hence, N when divided by 105 leaves the remainder as 104.

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