The product of two positive integers \(x\) and \(y\) is 6760 and their HCF is 13. How many such ordered pairs \((x, y)\) can be formed?
Question and options
The product of two positive integers and is 6760 and their HCF is 13. How many such ordered pairs can be formed?
- 4
- 3
- 2
- 1
Answer and explanation
Correct answer: A - 4
x = 13a, y = 13b with a, b coprime and ab = 6760/169 = 40. Coprime factorisations of 40: (1,40), (40,1), (5,8), (8,5). So 4 ordered pairs (x, y): (13,520), (520,13), (65,104), (104,65).
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