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The integer 120 has many factorizations. For example, 120 = (2)(60), 1

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parkhydel
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The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   27 Apr 2020, 15:52
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The integer 120 has many factorizations. For example, \(120 = (2)(60)\), \(120 = (3)(4)(10)\), and \(120 = (–1)(–3)(4)(10)\). In how many of the factorizations of 120 are the factors consecutive integers in ascending order?

A. 2
B. 3
C. 4
D. 5
E. 6


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C
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GaurSaini
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   01 May 2020, 21:35
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let's do prime factorization of 120 so that we can look into the possible solutions.

120 = 2^3*3*5

Looking at the factorization, we have 2,3,5 and power of 2.

Hence we can deduce that 2,3,4,5 are factors of 120.

Hence,
1. 1*2*3*4*5
2. 2*3*4*5
3. -5*-4*-3*-2
4. 4*5*6
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nick1816
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The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   27 Apr 2020, 16:18
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Minimum product of 6 consecutive positive numbers = 6!=720
So we can't write 120 as the product of 6 or more consecutive positive or negative integers

1. Product of minimum 5 positive integers = 5! = 120

120 = 1*2*3*4*5

2. \(3^4 < 120<4^4\)
Hence if 120 can be written as the product of 4 consecutive integers, then 3 and 4 must be included.

\(\frac{120}{3*4} = 10 =2*5\)

120 = 2*3*4*5 (since number of factors are even, we can change the signs of each factor and make another combination)

3. 120= -5*-4*-3*-2

4. \(4^3<120<5^3\)
Hence if 120 can be written as the product of 3 consecutive integers, then 4 and 5 must be included.

120/4*5 = 6

120= 4*5*6

\(10^2<120<11^2\)

10*11 is not equal to 120



C




parkhydel wrote:
The integer 120 has many factorizations. For example, \(120 = (2)(60)\), \(120 = (3)(4)(10)\), and \(120 = (–1)(–3)(4)(10)\). In how many of the factorizations of 120 are the factors consecutive integers in ascending order?

A. 2
B. 3
C. 4
D. 5
E. 6


PS62451.02
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RajatJ79
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   11 Jan 2021, 19:48
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plaverbach wrote:
Why not -4*-5*6?


Hey plaverbach , that's cause in -5, -4, 6 combination, -4 and 6 are not consecutive integers.

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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   23 Aug 2021, 20:24
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4 possibilities

1 2 3 4 5
-2 -3 -4 -5
4 5 6
-4 -5 -6
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TarunKumar1234
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   01 Sep 2021, 11:45
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120 = 1*2*3*4*5 (1 way) = 2*3*4*5 (2 ways, positive and negative orders) = 4*5*6 (1 way)

So, It is C.
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The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   08 Jan 2024, 07:49
I don't know why they wrote this sentence so horrible.
Quote:
In how many of the factorizations of 120 are the factors consecutive integers in ascending order?

Not even common in verbal section is inverted sentence.

Thanks to ChatGPT and here's a rephrased one.
Quote:
How many factorizations of 120 have consecutive integers as factors in ascending order?


120 = 1 × 2 × 3 × 4 × 5
120 = 2 × 3 × 4 × 5
120 = 4 × 5 × 6
120 = (–5) × (–4) × (–3) × (–2)

How many such factorizations?
Four.
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RitambharaJaiz
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   16 Mar 2024, 07:36
RajatJ79 wrote:
plaverbach wrote:
Why not -4*-5*6?

Hey plaverbach , that's cause in -5, -4, 6 combination, -4 and 6 are not consecutive integers.

Posted from my mobile device

­why not -4 , -5 , -6.....this is consecutive as well as in ascending order?
 
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Bunuel
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   16 Mar 2024, 07:44
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RitambharaJaiz wrote:
RajatJ79 wrote:
plaverbach wrote:
Why not -4*-5*6?

Hey plaverbach , that's cause in -5, -4, 6 combination, -4 and 6 are not consecutive integers.

Posted from my mobile device

­why not -4 , -5 , -6.....this is consecutive as well as in ascending order?

 

­
Their product is -120, not 120.
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   18 Mar 2024, 10:20
hello,
When you mentioned
120 = 1*2*3*4*5
Then the answer for consecutive integers in ascending order should be 5 so the answer should be D? I am confused can somebody explain this to me
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Bunuel
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   18 Mar 2024, 10:29
Expert Reply
 
mehul2494 wrote:
hello,
When you mentioned
120 = 1*2*3*4*5
Then the answer for consecutive integers in ascending order should be 5 so the answer should be D? I am confused can somebody explain this to me

­
Here are FOUR possible combinations:

1. \((-5)(-4)(-3)(-2)\)
2. \(1*2*3*4*5\)
2. \(2*3*4*5\)
4. \(4*5*6\)

What is the fifth one?­
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   21 Mar 2024, 05:35
How about 3*5*8 

3*40
8*15
5*24
2*5*12
3*4*10
2*4*15


Too many answers...
Bunuel wrote:
mehul2494 wrote:
hello,
When you mentioned
120 = 1*2*3*4*5
Then the answer for consecutive integers in ascending order should be 5 so the answer should be D? I am confused can somebody explain this to me

­
Here are FOUR possible combinations:


1. \((-5)(-4)(-3)(-2)\)
2. \(1*2*3*4*5\)
2. \(2*3*4*5\)
4. \(4*5*6\)

What is the fifth one?­

­
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Bunuel
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink] New post   21 Mar 2024, 07:01
Expert Reply
unicornilove wrote:
How about 3*5*8 

3*40
8*15
5*24
2*5*12
3*4*10
2*4*15


Too many answers...
Bunuel wrote:
mehul2494 wrote:
hello,
When you mentioned
120 = 1*2*3*4*5
Then the answer for consecutive integers in ascending order should be 5 so the answer should be D? I am confused can somebody explain this to me

­
Here are FOUR possible combinations:





1. \((-5)(-4)(-3)(-2)\)
2. \(1*2*3*4*5\)
2. \(2*3*4*5\)
4. \(4*5*6\)

What is the fifth one?­

­

­
You should read a question crefully:

The integer 120 has many factorizations. For example, \(120 = (2)(60)\), \(120 = (3)(4)(10)\), and \(120 = (–1)(–3)(4)(10)\). In how many of the factorizations of 120 are the factors consecutive integers in ascending order?

 ­
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Re: The integer 120 has many factorizations. For example, 120 = (2)(60), 1 [#permalink]
21 Mar 2024, 07:01
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