Question

Please help me with this.

Answer 1

`\displaystyle {y^4}`

Explanation:

The GCF of a set of numbers is the biggest divider that will divide all the numbers without leaving a remainder
As an example, the GCF of 4, 8 and 20 is 4, for 3, 4 and 5 it is 1 since there is no common factor

`\textrm {We have the three numbers as }`
`y^4, y^5 \;and\; y^(10)`

Which of these numbers will divide into each of these without leaving a remainder?

`\mathrm{The \:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)`

This means the smallest exponent value
`y^4` will be the GCF because

`(y^4)/(y^4) = 1\\\\(y^5)/(y^4) = y^(5-4)} = y^1\\\\(y^10)/(y^4) = y^(10-4)} = y^6\\\\\\`

So the general rule for finding the GCF of
`y^a, y^b \;and\; y^c is\\\\\mathrm {\;Choose\; the\; one \;with \;the \;lowest \;exponent \;value \;among \;exponents\; a, \;b \;and\; c}`