The product of two positive whole numbers is 456 and their difference is 5. What is the bigger number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
The two numbers are factors of 456 that differ by 5, so 456 is split into its prime factors and the factor pairs are listed.
\(456=2^{3}\times3\times19\)
Factor pairs: \(1\times456\), \(2\times228\), \(3\times152\), \(4\times114\), \(6\times76\), \(8\times57\), \(12\times38\), \(19\times24\)
Only \(24-19=5\)
The numbers are 19 and 24, so the bigger number is 24.
Why the other options are incorrect
Option (1) 29 — Incorrect. 29 does not divide 456 exactly, so it cannot be one of the numbers.
Option (2) 19 — Incorrect. 19 is the smaller of the two numbers.
Option (3) 38 — Incorrect. \(456\div38=12\), and \(38-12=26\), not 5.