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Leno4ka [110]
3 years ago
14

Write the prime factorization for 65,169

Mathematics
1 answer:
posledela3 years ago
8 0

Let's try to find some primes that divide this number.

The number is not divisible by 2, because it is odd.

The number is divisible by 3 though, because the sum of its digits is:

6+5+1+6+9=27=3\cdot 9

So, we can divide the number by 3 and keep going with the factorization:

65169\div 3 = 21723

This number is again divisible by 3, because

2+1+7+2+3 = 15 = 3\cdot 5

We have

21723\div 3 = 7241

This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have

7241\div 13 = 557

And 557 is prime, so we're done. This means that the prime factorization of 65169 is

3^2\cdot 13 \cdot 557

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Answer:

2x+y=15x+y=10

Consider the first equation. Subtract 15x from both sides.

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Combine 2x and −15x to get −13x.

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