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What are two numbers that have a GCF of 55?

Updated: 10/31/2022

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13y ago

55 and 110

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13y ago

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Q: What are two numbers that have a GCF of 55?
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LCM of two numbers is 450. The GCF of the two numbers is 5. The two numbers add up to 55. What are the two numbers?

For any two natural numbers a and b:Product of a and b = LCM(a,b) x GCF(a,b)Let one of the numbers be y, then other number = (55 - y)So,y(55 - y) = 450 x 555y - y2 = 2250On solving the equation we gety = 5/2(11 &Acirc;&plusmn; i(239)1/2)where i = (-1)1/2Solutions of the given equation are two complex numbers but according to question we need natural numbers. Since GCF and LCM are defined for natural numbers then there exists no value of y for which the given conditions are true.