Complete the factor tree.
So at the top, we have the number 462. And if we look down at the bottom, we have that 462 is equal to 11 times some number that we don’t know times seven times two. And a factor tree helps us figure that out.
So to begin, 462 is equal to 33 times some number. So to figure that out, we simply need to take 462 and divide by 33. This will give us that number, and it’s equal to 14. And we can double-check this because, below that, 14 is equal to seven times two, which is true. So over by the 33, 33 is equal to some number times three. So to find that number, we need to take 33 and divide by three, which gives us 11. So 11 times three is equal to 33.
So now the factor tree is complete, but how do we know? The reason why we know is because 11, three, seven, and two are all prime, meaning it’s only divisible by itself and one, so there wouldn’t be any more tree branches to break it up, because it will just be one times itself. So notice these numbers at the bottom.
Now that we are complete, we’ll actually multiply to equal 462. So to complete the bottom, 462 is equal to 11 times three times seven times two. So now our factor tree is complete. So our first blank we filled in 14. This blank we filled in 11. And this blank we filled in a three. So these will be our final answers.