Question

Let abc be a 3 digit no. With nonzero digits such that a2+b2=c2.what is the largest possible prime factor of abc
?

Answer 1

Answer:

29

Step-by-step explanation:

Three digit number = abc (Given)

The largest possible prime factor of abc is  a² + b² = c²

where a b c are the single digits. Let a be 3 b be 4 and c be 5.

Thus, the only possible solution will be -

5² = 3² + 4²

25 = 9 + 16

25 = 25

Both being equal, thus -

abc  = 345  or 435

345 = 3 × 5 × 23

435 = 3 × 5 × 29

Thus the largest possible prime factor of abc  is 29

Answer 2

Answer:

Step-by-step explanation:

Three digit number = abc (Given)

The largest possible prime factor of abc is a² + b² = c²

where a b c are the single digits. Let a be 3 b be 4 and c be 5.

Thus, the only possible solution will be -

5² = 3² + 4²

25 = 9 + 16

25 = 25

Both being equal, thus -

abc = 345 or 435

345 = 3 × 5 × 23

435 = 3 × 5 × 29

Thus the largest possible prime factor of abc is 29