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# number theory

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Find the smallest positive integer such that the product of its digits is 60.

Jun 27, 2022

#1
+2602
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The prime factorization of 60 is: $$2^2 \times 5 \times 3$$.

The largest single-digit factor of 60 is 6. This will be our unit digit.

This means the remaining numbers must multiply out to 10, which means we need a 2 and 5.

Now, what's the smallest number possible with these 3 digits?

Jun 27, 2022

#1
+2602
0

The prime factorization of 60 is: $$2^2 \times 5 \times 3$$.

The largest single-digit factor of 60 is 6. This will be our unit digit.

This means the remaining numbers must multiply out to 10, which means we need a 2 and 5.

Now, what's the smallest number possible with these 3 digits?

BuilderBoi Jun 27, 2022