</span>The <span>common factors</span><span> for </span><span>32,48</span><span> are </span><span><span>−16,−8,−4,−2,−1,1,2,4,8,16</span>.</span><span>−16,−8,−4,−2,−1,1,2,4,8,16 </span> The GCF<span> of numerical </span>factors <span>−16,−8,−4,−2,−1,1,2,4,8,16</span><span> is </span><span>16.
Turn each number into the product of it's prime factors.
32=16x2=2x2x2x2x2=2^5
48=24*2=6x4x2=2x3x2x2x2
Pick the highest number that occurs. In this case it is 2. Now we have to see how many times it appears in both. It appears 5 times in 32 and 4 times in 48. 4 is the highest number of times it appears in the numbers so:
2^4=2x2x2x2=16
The Greatest Common Factor (GCF) of 32 and 48 is 16.
A dilation is one type of transformation that is applied to images, in which the side lengths are multiplied by a constant called scale factor, changing the side lengths of the image.
In item a, the initial length was of 11 and the final length is of 71, hence the multiplier, which is the scale factor, is given as follows:
71/11 = 6.45.
In item b, the initial length was of 16 and the final length was of 23, hence the scale factor is given as follows:
23/16 = 1.4375.
For item 3, the multiplier is a number that is less than 1, meaning that the image is smaller than the pre-image.
