A * B = 100,000
Two numbers with no zeros in their make-up can be multiplied
to create 10,000. They are 625 and 16. It is also possible to have two
numbers multiplied together with no zeros that equal 100,000 and
1,000,000? What are each of these pairs?
to create 10,000. They are 625 and 16. It is also possible to have two
numbers multiplied together with no zeros that equal 100,000 and
1,000,000? What are each of these pairs?
posted by Ragknot at
6:12 PM
14 Comments:
3125*32=5^5*2^5=(5*2)^5=10^5=100,000
15625*64=5^6*2^6=(5*2)^6=10^6=1,000,000
3125 and 32 will make 100000
512 * 1953125 = 1,000,000,000
oops did a billion
ah, I saw your answer, and thought .. I don't remember computing that one. I didn't figure a billion.
This one is very easy. I dont even need to tell the answer, but the explanation is enough..
To make 10,000.. 625 and 16 are multiplied.
To make 100,000 (which is 10,000* 5*2), take 625*5 and 16*2.
Same way, for 1,000,000 (which is 100,000*5*2), take 625*5*5 and 16*2*2.
Either way there are no zero in the make-up of the factors.
-3125 and -32 and -15625 and -64 are also solutions.
gotta love the negative numbers
To figure any of these out, prime factorization can be used. Because any number with the restraints as those above (starts with a one and then contains any number of zeroes and only zeroes), each number can be written as 10^n where n is any whole number. The prime factorization for 10 is 2*5, thus the prime factorization of (10^n) is (2^n)(5^n)
Also keep in mind that any multiple of 2 multiplied with any multiple of 5 will equal a number ending in a 0. Therefore, the pairs of numbers are 2^n and 5^n where the n=the power 10 is raised to to get the given number.
Incidentally, there is NO such pair that equals 100,000,000 or 10,000,000,000, because 5^8 = 390625 and 2^10 = 1024, each of which "has a zero in its makeup".
And there are many such exceptions. In fact, the larger you go, the more often they happen...
Very true. I did not even think about that. I had just assumed that the only restriction was it could not end in a zero.
3125*32 will be the ans...
3125 * 32 = 100000
15625 * 64 = 1000000
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