Review Which is the smallest number to be divided to make 153664 as a perfect cube?
Mẹo Hướng dẫn Which is the smallest number to be divided to make 153664 as a perfect cube? Mới Nhất
Bùi An Phú đang tìm kiếm từ khóa Which is the smallest number to be divided to make 153664 as a perfect cube? được Cập Nhật vào lúc : 2022-12-26 00:50:08 . Với phương châm chia sẻ Mẹo về trong nội dung bài viết một cách Chi Tiết Mới Nhất. Nếu sau khi Read nội dung bài viết vẫn ko hiểu thì hoàn toàn có thể lại Comment ở cuối bài để Mình lý giải và hướng dẫn lại nha.Hint: A perfect cube is an integer which is equal to another integer raised to the power 3. For example 125 is a perfect cube as it can be written as $ 5^3 $ , 5 raised to the power 3. So divide 3600 by every given option and if the result obtained can be written as a perfect cube then that particular option is our answer.
Complete step-by-step answer:
We are given to determine the smallest number by which 3600 can be divided to make it a perfect cube.
First one is 9, when 3600 is divided by 9 we get $ dfrac36009 = 400 $ . But 400 is a perfect square of 20 but not a perfect cube.
Second one is 50, when 3600 is divided by 50 we get $ dfrac360050 = 72 $ . 72 cannot be written as a perfect cube.
Third one is 300, when 3600 is divided by 300 we get $ dfrac3600300 = 12 $ . 12 is not a perfect cube.
Fourth one is 450, when 3600 is divided by 450 we get $ dfrac3600450 = 8 $ . 8 can also be written as 2 raised to the power 3.
This means that 8 is a perfect cube of 2. So 3600 must be divided by 450 to make it a perfect cube
So, the correct answer is “Option D”.
- What should be divided from 1536 to get a perfect cube?What is the smallest number by which be divided to make it a perfect cube?What should be divided by 53240 to make it a perfect a cube *?What should be divided by 625 to make it a perfect cube?
Note: Another approach
First we have to factorize 3600.
3600 can also be written $ 2 times 2 times 2 times 2 times 3 times 3 times 5 times 5 $
As we can see in the prime factorization of 3600, there is a repeated factor 2 for four times and remaining factors are repeated less than 3 times.
For a perfect cube there must be a repeating factor for 3 times.
So 3600 must be divided by $ 2 times 3 times 3 times 5 times 5 $ to give a perfect cube $ 2 times 2 times 2 = 8 $
And $ 2 times 3 times 3 times 5 times 5 = 450 $
So 3600 must be divided by 450 to give a perfect cube 8.
Given: A number $6912$.
To do: To find the smallest number by which $6912$ must be divided so that the number formed is a perfect cube.
Solution:
The factors of:
$6912=underline2times2times2timesunderline2times2times2times2times2timesunderline3times3times3=2^2times2^6times3^3$
Therefore, we should divide $6912$ by $2^2=4$, the smallest number to get $1728$ which is a cube of $12$.
(i) We have,
1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
After grouping the prime factors in triplets, it’s seen that one factor 3 is left without grouping.
1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3
So, in order to make it a perfect cube, it must be divided by 3.
Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3.
(ii) We have,
10985 = 5 × 13 × 13 × 13
After grouping the prime factors in triplet, it’s seen that one factor 5 is left without grouping.
10985 = 5 × (13 × 13 × 13)
So, it must be divided by 5 in order to get a perfect cube.
Thus, the required smallest number is 5.
(iii) We have,
28672 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7
After grouping the prime factors in triplets, it’s seen that one factor 7 is left without grouping.
28672 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 7
So, it must be divided by 7 in order to get a perfect cube.
Thus, the required smallest number is 7.
(iv) 13718 = 2 × 19 × 19 × 19
After grouping the prime factors in triplets, it’s seen that one factor 2 is left without grouping.
13718 = 2 × (19 × 19 × 19)
So, it must be divided by 2 in order to get a perfect cube.
Thus, the required smallest number is 2.
What should be divided from 1536 to get a perfect cube?
Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3. Was this answer helpful?What is the smallest number by which be divided to make it a perfect cube?
So, it must be divided by 2 in order to get a perfect cube. Thus, the required smallest number is 2.What should be divided by 53240 to make it a perfect a cube *?
∴ The smallest number by which 53240 should be divided to make it a perfect cube is 5. Was this answer helpful?What should be divided by 625 to make it a perfect cube?
∴ The smallest number by which the number 625 must be divided to obtain a perfect cube is 5. Tải thêm tài liệu liên quan đến nội dung bài viết Which is the smallest number to be divided to make 153664 as a perfect cube?
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