When a number is divided by 2 the remainder is 1. When the same number is divided by 3, 4, and 5 the remainder are 2, 3, and 4 . Calculate using equation

Question

 Please calculate the least number using mathematical or algebraic equation, thanks for answering this question...

 

Answer 1

if N leaves a remainder of 1 when divided by 2, then N+1 must be divisible by 2

if N leaves a remainder of 2 when divided by 3, then N+1 must be divisible by 3

if N leaves a remainder of 3 when divided by 4, then N+1 must be divisible by 4

if N leaves a remainder of 4 when divided by 5, then N+1 must be divisible by 5

so, N+1 must be a multiple of 2, 3, 4, and 5

eliminate the 2 because it is a factor of 4

N+1 must be a multiple of 3, 4, and 5

N+1 must be 3*4*5=60

therefore N must be 60-1=59 which is the least number satisfying the above conditions

Answer 2

By the remainder theorem, f(x) = r.

f(2) = 1; f(3) = 2; f(4) = 3; f(5) = 4

P1 = (2,1); P2 = (3,2); P3 = (4,3); P4 = (5,4)

m = Δy/Δx = 1

y - y1 = m(x - x1)

y = x - 1

A2