Answer:
[tex]\displaystyle {y^4}[/tex]
Step-by-step 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
[tex]\textrm {We have the three numbers as }[/tex] [tex]y^4, y^5 \;and\; y^{10}[/tex]
Which of these numbers will divide into each of these without leaving a remainder?
[tex]\mathrm{The \:exponent\:rule}:\quad \dfrac{x^a}{x^b}=x^{a-b}[/tex]
This means the smallest exponent value [tex]y^4[/tex] will be the GCF because
[tex]\dfrac{y^4}{y^4} = 1\\\\\dfrac{y^5}{y^4} = y^{5-4}} = y^1\\\\\dfrac{y^10}{y^4} = y^{10-4}} = y^6\\\\\\[/tex]
So the general rule for finding the GCF of [tex]y^a, y^b \;and\; y^c is\\\\\mathrm {\;Choose\; the\; one \;with \;the \;lowest \;exponent \;value \;among \;exponents\; a, \;b \;and\; c}[/tex]
