Timemagazine
New Member
- Joined
- Oct 11, 2008
- Messages
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- HSC
- 2004
Hi peeps,
Just one small question, from AMC - Problem: 2000 = 2^4 x 5^3 is the product of 7 prime factors. X = smallest integer greater than 2000 with his property and y be the largest integer smaller than 2000 with this property. Value of x - y?
Someone told me this way and I need some explanation to what it means:
2^e x 3^f x 5^g x 7^h.... - 2^i x 2^j x 2^k x 2^l... = 64 (2^6)
Then he wrote,
2 x 3 x 5 x 7.... - 2 x 3 7^2 = 2(2x3....)
Then,
2^a x (p) - 2^a x (p+2) where p is prime = 2 (2^a) = 128
Deducing 2^6 x 3 - 2^7 = 64
Could someone please explain what this all means in context to the question? I understand it but I forget it from time to time...
Ciao, Timemagazine Express
Just one small question, from AMC - Problem: 2000 = 2^4 x 5^3 is the product of 7 prime factors. X = smallest integer greater than 2000 with his property and y be the largest integer smaller than 2000 with this property. Value of x - y?
Someone told me this way and I need some explanation to what it means:
2^e x 3^f x 5^g x 7^h.... - 2^i x 2^j x 2^k x 2^l... = 64 (2^6)
Then he wrote,
2 x 3 x 5 x 7.... - 2 x 3 7^2 = 2(2x3....)
Then,
2^a x (p) - 2^a x (p+2) where p is prime = 2 (2^a) = 128
Deducing 2^6 x 3 - 2^7 = 64
Could someone please explain what this all means in context to the question? I understand it but I forget it from time to time...
Ciao, Timemagazine Express
