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Please help (10 points) thankyou

Please help (10 points) thankyou-example-1
User MShah
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Take the prime factorizations of each given number. For example, in (a) we have


\mathrm{gcf}(40,60)=20

because we can write
40=2^3\cdot5 and
60=2^2\cdot3\cdot5, and the largest number that we can divide both numbers by with no remainder is
2^2\cdot5=20. When we do this division, we have
(2^3\cdot5)/(2^2\cdot5)=2 and
(2^2\cdot3\cdot5)/(2^2\cdot5)=3. The numbers 2 and 3 share no common factors.

Then for (b),


\mathrm{gcf}(24,36)=\mathrm{gcf}(2^3\cdot3,2^2\cdot3^2)=2^2\cdot3=12

and for (c),


\mathrm{gcf}(18,45,90)=\mathrm{gcf}(2\cdot3^2,3^2\cdot5,2\cdot3^2\cdot5)=3^2=9

User Kuldeep Bhimte
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