Question

Please help (10 points) thankyou

Answer 1

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`