Question

What is the greatest common factor of x6 and x9

Answer 1

Answer:

x⁶  

Step-by-step explanation:

Factors of x⁶ = x · x · x · x · x · x               = x⁶

Factors of x⁹ = x · x · x · x · x · x · x · x · x = x⁶·x³

The greatest common factor of x⁶ and x⁹ is x⁶.

Answer 2

Greatest common factor is the factor which is greatest among all common factors. The greatest common factor of $x^6$ and $x^9$ is

How to find Greatest common factor?

Greatest common factor, as the name implies, is greatest among all common factors among the quantities given.

We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).

For the given case, the two quantities can be rewritten as:

$x^6 = x \times x \times x \times x \times x \times x\\\\x^9 = x \times x \times x \times x \times x \times x \times x \times x \times x$

Taking 6 of x common is the maximum common factors we can take out from both of them, thus, $x \times x \times x \times x \times x \times x = x^6$ is the GCF of both given quantities.

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