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If the greatest common factor of 2 numbers is 6 and each number is between 25 and 40, what are the 2 numbers, and how do you know?

User Dwrbudr
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1 Answer

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Explanation:

the GCF is the product of all prime factors the numbers have in common.

a prime factor is a prime number that the number can be divided by without any remains.

the prime numbers start at 2.

so : 2, 3, 5, 7, 11, ...

for two numbers x, y having the GCF of 6 means they only have 2 and 3 as prime factor in common.

x = 2×3×a

y = 2×3×b

a <> b (otherwise there would be an additional shared prime factor)

what a and b factors can be found, so that x and y are between 25 and 40 ?

2×3 × 2 = 12 no

2×3 × 3 = 18 no

2×3 × 4 = 24 no

2×3 × 5 = 30 yes

2×3 × 6 = 36 yes

2×3 × 7 = 42 no

so, to verify

30 = 2×3×5

36 = 2×2×3×3

the prime factors they have in common are therefore one time 2 and one time 3 (2×3 = 6).

correct.

so, the two numbers are 30 and 36.

and because of our verification we know and are sure.

User Gary Van Der Merwe
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