Find The Remainder

Number Theory Level 1

Find the remainder when 289 is divided by 89?


The answer is 22.

Aditya Raj by Aditya Raj , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Mohammad Khaza
Aug 4, 2017

3 × 9 = 27 3 \times 9=27

s o , 89 × 3 so, 89 \times 3 = 27 × 10 − 3 27 \times 10-3 = 267 267

so, the remainder is=289-267=22 \text{so, the remainder is=289-267=22}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Daniel Barnhurst
Nov 21, 2014

89 × 3 = 267 \Large 89 \times 3 = 267

So if you subtract that from 289 289 you get:

289 − 267 = 22 \Large 289 - 267 = 22

So, since you can no longer subtract 89 89 from the number,

289 m o d 89 = 22 \Large 289 \bmod 89 = 22

1 Helpful 0 Interesting 0 Brilliant 0 Confused

289 ≡ 200 + 89 ≡ 200 ≡ 100 + 100 ≡ 11 + 11 ≡ 22 ( m o d ⁣ 89 ) 289\equiv 200+89\equiv 200\equiv 100+100\equiv 11+11\equiv 22\pmod{\!89}

mathh mathh - 6 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...