What is BA?

Number Theory Level 2

Given A and B are two non-zero digits and the 2-digit numbers formed by these two digits have the following properties:

AB is divisible by 17;

BA is a product of 2 odd prime numbers;

Find the 2-digit number BA .

58 85 15 51

Kelp_ Huan by kelp_ huan , 14, China

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

Frisk Dreemurr
Aug 2, 2020

AB \text{AB} is a number divisible by 17 17

BA \text{BA} is a product of 2 2 odd prime numbers

Possible values for AB \text{Possible values for AB} Possible values for A \text{Possible values for A} Possible values for B \text{Possible values for B} Possible values for BA \text{Possible values for BA} Factorization \text{Factorization}
17 17 1 1 7 7 71 71 71 ¹ 71¹
34 34 3 3 4 4 43 43 43 ¹ 43¹
51 51 5 5 1 1 15 15 3 ¹ × 5 ¹ \color{#20A900}3¹ × 5¹
68 68 6 6 8 8 86 86 2 ¹ × 43 ¹ 2¹ × 43¹
85 85 8 8 5 5 58 58 2 ¹ × 29 ¹ 2¹ × 29¹

Therefore, the two digit number should be 15 \text{Therefore, the two digit number should be }\color{#20A900}\boxed{15}

0 Helpful 0 Interesting 1 Brilliant 0 Confused
Kelp_ Huan
Aug 1, 2020

AB is divisible by 17. The possible numbers are 17, 34, 51, 68, 85 BA is the product of 2 odd primes the only possible number BA is 15

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...