JPEG: In image compression why are higher frequency components divided by a larger number during quantization
Note that the matrix which divides the DCT coefficients, performs quantization and the larger the divisor the coarser will be the step size at that frequency.

And that's the very essence of the perceptive image coding, where less perceived (roughly less important) content is coarsely quantized while the more important and dominant low frequency content is finely quantized and represented better. This will result in more quantized zeros at high frequencies which eventually yield more compression while maintaining less distortion compared to a uniform quantization. 

Hence this takes advantage of human perception characteristics. Had you thrown away the low frequency information most people would object immediately to the result, while they would not even recognize the loss of high frequency information until some aggressive threshold.