If the product of two numbers is 578 and their Highest Common Factor (HCF) is…
2021
If the product of two numbers is 578 and their Highest Common Factor (HCF) is 17, then what is the difference between the two numbers?
- A.
17
- B.
34
- C.
51
- D.
68
Attempted by 122 students.
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Correct answer: A
Key idea: express the numbers as multiples of the HCF.
Let the numbers be 17a and 17b, where gcd(a,b) = 1.
Their product is (17a)(17b) = 289ab, so 289ab = 578 and therefore ab = 578/289 = 2.
Find coprime factors of 2: a = 1 and b = 2.
So the numbers are 17×1 = 17 and 17×2 = 34. Their difference is 34 − 17 = 17.
Answer: 17