sum of the largest and smallest prime factors

Question

I got different answer from the answer sheet which says the answer is 14. What is the easiest way to find the largest prime factors of 5445?

What is the sum of the largest and smallest prime factors of 5445?

What answer did you get? (14 is correct.) – quid Sep 05 '16 at 13:44 — quid, Sep 05 '16 at 13:44

score 1 · Answer 1 · answered Sep 05 '16 at 13:54

Here's how I'd go about it:

$5445$ ends in $5$ so we know that's one prime factor. In fact $5445=5500-55=5(1100-11)=5\cdot1089$
If we look at $1089$ and add up the digits, we have $1+0+8+9=2\cdot9$. We can use the fact that the sum of a numbers digits are divisible by $9$ iff the number is too. So $1089=999+90=9\cdot(111+10)=9\cdot121$. Recall that $9=3^2$ so we've just found two more factors.
Looking at $121$ we can recall that it's $11^2$

So we can factor $5445$ as $5\cdot3^2\cdot11^2$. So our answer's $3+11=14$.

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