Question

Two positive integers multiply to 5070, with their highest common factor being 13 and their sum amounting to 143. What is the difference between these two integers?

Q: Answer-Two positive integers multiply to 5070, with their highest common factor being 13 and their sum amou...

Let the two numbers be 13a and 13b ATQ 13a 13b 5070 So, a b 30 . 1 Also, 13a 13b 143 So, a b 11 Or, a 11 b ... 2 Putting value of a in equation 1, we have 11 b b 30 Or, 11b b2 30 Or, b2 11b 30 0 Or, b2 6b 5b 30 0 Or, bb 6 5b 6 0 Or, b 6b 5 0 So, b 6 or b 5 So, the two numbers are 13 5 65 and 13 6 78 Required difference 78 - 65 13