 # Question

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14700 = 2 x 2 x 3 x 5 x 5 x 7 x 7

The statement “greatest number that will divide…. is 70” means 70 is the HCF.

And 70 = 2 x 5 x 7

Rewriting:

37800           = 70 x 540 = (2 x 5 x 7) x (2 x 3 x 5   x 2 x 3 x 3)

14700           = 70 x 210 = (2 x 5 x 7) x (2 x 3 x 5   x 7)

unknown x    = 70 x (? ) = (2 x 5 x 7) x (*a factor not consisting of 2, 3, 5 or any combination of these)

*The unknown number x will have a factor 70, and beyond this factor 70, it cannot have 2 or 3 or 5 or any combination of these 3 factors. Else HCF will be bigger than 70. For example,

if x = 140 = 70×2, then HCF is 140 (all three numbers can be divided by 140).

If x = 210 = 70×3, then HCF is 210 (all three numbers can be divided by 210)

… and so 70×5, 70×6, 70×10, 70×15, 70×30 are all not possible values of x.

The additional factors beyond factor 70 must sort of restrict the HCF at 70.

Answer: can pick any two possible values of x below:

(a) 70   = 70 x 1 (“giving-mark” answer)

(b) 490 = 70 x 7 (because 37800 has no more additional factor 7 beyond factor 70)

(c) 770 = 70 x 11 (because both 37800 and 14700 have no factor 11)

(d) 910 = 70 x 13 (because both 37800 and 14700 have no factor 13) …. and so on for 70 times other bigger prime numbers

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