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