Factor Trees for 240:

Because 240 has so many factors, it is possible to make MANY different cistron trees that create a forest of 240 gene trees. This post simply contains eleven of those many possibilities. The two trees beneath demonstrate different permutations that can be made from the aforementioned bones tree. The mirror images of both, as well as mirror images of parts of either tree, would be other permutations.

240 Factor Trees

A expert way to make a gene tree for a composite number is to brainstorm with one of its factor pairs so make factor trees for the blended numbers in that cistron pair.

240 Factor Trees 1 - 3

In this commencement set up of three cistron copse we can besides run across the factor trees for 120, eighty, 4, & 60.

240 Factor Trees 4 - 6

These 3 factor trees likewise include factor trees for 48, 6, 40, viii, and thirty.

240 Factor Trees 7 - 9

Finally, these three gene copse as well include factor copse for 10, 24, 12, 20, 15, and sixteen.

This wood of 240 factor trees is dedicated to Joseph Nebus. Read the comments to his post, You might also like, because, I don't know why, to discover why I was inspired to create images of parts of this woods.

Factors of 240:

  • 240 is a blended number.
  • Prime factorization: 240 = 2 x 2 ten ii x 2 x 3 x 5, which can be written 2⁴ x iii x five
  • The exponents in the prime factorization are 4, 1 and 1. Adding one to each and multiplying nosotros get (4 + ane)(1 + i)(ane + 1) = 5 x ii 10 2 = twenty. Therefore 240 has twenty factors.
  • Factors of 240: one, 2, 3, 4, 5, 6, eight, 10, 12, fifteen, 16, 20, 24, 30, 40, 48, 60, eighty, 120, 240
  • Gene pairs: 240 = 1 x 240, 2 x 120, 3 10 80, 4 x lx, five x 48, 6 ten 40, 8 x thirty, 10 x 24, 12 x 20, or fifteen x 16
  • Taking the cistron pair with the largest square number cistron, we get √240 = (√16)(√xv) = 4√xv ≈ fifteen.492

Sum-Difference Puzzle:

60 has 6 factor pairs. One of those factor pairs adds up to 17, and a different ane subtracts to 17. Can you detect those factor pairs to solve the beginning puzzle beneath?

240 has x factor pairs. One of them adds upwardly to 34, and some other ane subtracts to 34. If you lot tin identify those factor pairs, so you tin can solve the second puzzle.

The second puzzle is actually just the get-go puzzle in disguise. Why would I say that?

Another Fact about the Number 240:

2 + 4 + 6 + 8 + ten + 12 + 14 + sixteen + 18 + 20 + 22 + 24 + 26 + 28 + xxx = 240; that'due south the sum of the starting time fifteen fifty-fifty numbers.