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What is the lowest positive integer that is divisible by both 5,000,00
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24 Jun 2021, 09:39
24 Jun 2021, 09:39
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76% (01:29) correct
23% (01:45) wrong based on 26 sessions
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What is the lowest positive integer that is divisible by both 5,000,000 and 256?
A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000
A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000
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Re: What is the lowest positive integer that is divisible by both 5,000,00
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24 Jun 2021, 09:42
24 Jun 2021, 09:42
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Carcass wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?
A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000
A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000
-----ASIDE---------------------
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Consider these examples:
24 is divisible by 3 because 24 = (2)(2)(2)(3)
Likewise, 70 is divisible by 5 because 70 = (2)(5)(7)
And 112 is divisible by 8 because 112 = (2)(2)(2)(2)(7)
And 630 is divisible by 15 because 630 = (2)(3)(3)(5)(7)
-----ONTO THE QUESTION!---------------------
We can already see that all 5 answer choices are multiples of 5,000,000.
So it really comes down to which number is the smallest number that is divisible by 256.
256 = (2)(2)(2)(2)(2)(2)(2)(2)
So, the correct answer will be the smallest number that has eight 2's in its prime factorization
A) 5,000,000 = (5^7)(2^6), which means 5,000,000 has six 2's in its prime factorization
B) 10,000,000 = (5^7)(2^7), which means 5,000,000 has seven 2's in its prime factorization
C) 20,000,000 = (5^7)(2^8), which means 5,000,000 has EIGHT 2's in its prime factorization
Answer: C
Re: What is the lowest positive integer that is divisible by both 5,000,00
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09 Aug 2023, 05:07
09 Aug 2023, 05:07
1
We are looking for the LCM.
256 is 2^8
And 5,000,000 can be rewritten as 5*10^6, or 5^7*2^6.
The LCM of (256, 5,000,000) is therefore: 2^8*5^7
Which is the same as 10^7*2, or 20,000,000. Answer choice C is correct.
256 is 2^8
And 5,000,000 can be rewritten as 5*10^6, or 5^7*2^6.
The LCM of (256, 5,000,000) is therefore: 2^8*5^7
Which is the same as 10^7*2, or 20,000,000. Answer choice C is correct.
