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Secondary 1 | Maths
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Su
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Secondary 1 chevron_right Maths chevron_right Singapore

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Date Posted: 4 years ago
Views: 194
J
J
4 years ago
6804/x = y²

So 6804 = xy²

Now, find the prime factors of 6804.
We do so as we can then determine how the factors should be recombined to form our required integers.

6804 ÷ 2 = 3402
3402 ÷ 2 = 1701
1701 ÷ 3 = 567
567 ÷ 3 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7

7 cannot be divided by anything else other than itself or 1. It's a prime number. So we are done with the prime factorisation.


So 6804 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 7
= 2² × 3^5 × 7

There's a y² on the right hand side. So there must be an integer that is squared.
And we want it as big as possible.

Looking at the prime factors,


We have one 2s, five 3s, one 7.

We can assign one 2 and two 3s for each y.

That's the biggest number we can form for y, such that it can be squared.

Combining them for each y,
2 × 3 × 3 = 18

We are left with one 3 and one 7 to be combined. 3 × 7 = 21

Rearranging,

6804 = (3 × 7) × (2 × 3 × 3) × (2 × 3 × 3)

= 21 × 18 × 18

= 21 × 18²

Compare this to 6804 = xy²,

Your x is 21 and your y is 18