Question

The numbers are between 20 and 44.
Both numbers are multiples of 6 and are factors of 72.
Find the numbers that Nora is thinking
of.give the explanation

Answer 1

Answer: The numbers are 24 and 36

Explanation:

Let us consider the two numbers to be x and y

6 prime factorized can be written as 2×3

and 72 prime factorized can be written as 2³×3²

Prime factorization of both numbers x and y would contain 2×3 and let a and b be the product of rest of the numbers' prime factorized state

x = 2 × 3 × a

y = 2 × 3 × b

a and b must be a factor of (2³×3²)/(2×3) = 2²×3 which means the larger power of 2 and 3 in both numbers are 2 and 1

Since 20÷6 = 2$\frac{1}{3}$, both a and b must be numbers larger than 2$\frac{1}{3}$

and since 44÷6 = 7$\frac{1}{3}$, both a and b must be numbers smaller than 7$\frac{1}{3}$

The only possible combination is a = 2² and b = 2×3

Hence the numbers are

x = 2×3×2² = 24

y = 2×3×2×3 = 36

Hope my answer was of help :)