Product of all even divisors of 1000
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Answered by
4
down vote
accepted
First consider the prime factorization of 10001000. We have:
1000=23×53
1000=23×53
Now, how can we list all the factors of 10001000? We see that we can try listing them in a table:
20212223501248515102040522550100200531252505001000
50515253201525125212105025022420100500238402001000
We see that we can take (21+22+23)×(50+51+52+53)=2184(21+22+23)×(50+51+52+53)=2184. To get the sum of all factors, we would also include 2020 on the left side of the multiplication. We exclude 2020 because those would be odd factors.
accepted
First consider the prime factorization of 10001000. We have:
1000=23×53
1000=23×53
Now, how can we list all the factors of 10001000? We see that we can try listing them in a table:
20212223501248515102040522550100200531252505001000
50515253201525125212105025022420100500238402001000
We see that we can take (21+22+23)×(50+51+52+53)=2184(21+22+23)×(50+51+52+53)=2184. To get the sum of all factors, we would also include 2020 on the left side of the multiplication. We exclude 2020 because those would be odd factors.
vipulvikramiitp3bct3:
The question is asking for the product of even divisors, not the sum.
Ok
Thanx
Answered by
18
1000 = 2*2*2*5*5*5
Even divisors = 2, 4, 8, 2*5, 4*5, 8*5, 2*25, 4*25, 8*25, 2*125, 4*125, 8*125
Product of Even Divisors = 64^4 * 5^3 * 25^3 * 125^3 = 6.4*10^19
Even divisors = 2, 4, 8, 2*5, 4*5, 8*5, 2*25, 4*25, 8*25, 2*125, 4*125, 8*125
Product of Even Divisors = 64^4 * 5^3 * 25^3 * 125^3 = 6.4*10^19
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