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## Mẹo Hướng dẫn What is the smallest number with which 7803 must be divided so that the quotient is a perfect cube also find the cube root of the question thus obtain… Chi Tiết

Quý khách đang tìm kiếm từ khóa What is the smallest number with which 7803 must be divided so that the quotient is a perfect cube also find the cube root of the question thus obtain… được Cập Nhật vào lúc : 2022-10-09 11:54:42 . Với phương châm chia sẻ Thủ Thuật về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read nội dung bài viết vẫn ko hiểu thì hoàn toàn có thể lại Comment ở cuối bài để Ad lý giải và hướng dẫn lại nha.

(i) We have,

Nội dung chính

What smallest number should 7803 be multiplied with so that the product becomes a perfect cube ?`?What is the smallest number by which 6912 must be divided to make it a perfect cube?What is the smallest number by which 10976 must be divided to make it a perfect cube?What is the smallest number with which 7803 must be divided so that the quotient is a perfect cube?

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.

(i) 675

Prime factors of 675 = 3 × 3 × 3 × 5 × 5 = 33 × 52

We find that 675 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 52 = 25, which gives 27 as quotient and we know that 27 is a perfect cube .

(ii) 8640

Prime factors of 8640 = 2 × 2 × 2 × 2
× 2 × 2 × 3 × 3 × 3 × 5 = 23 × 23 × 33 × 5

We find that 8640 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 5 , which gives 1728 as quotient and we know that 1728 is a perfect cube.

(iii) 1600

Prime factors of 1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 = 23 × 23 × 52

We
find that 1600 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 52 = 25, which gives 64 as quotient and we know that 64 is a perfect cube

(iv) 8788

Prime factors of 8788 = 2 × 2 × 13 × 13 × 13 = 22 × 133

We find that 8788 is not a perfect cube.

Hence, for making the quotient a perfect cube we
divide it by 4, which gives 2197 as quotient and we know that 2197 is a perfect cube

(v) 7803

Prime factors of 7803 = 3 × 3 × 3 × 17 × 17 = 33 × 172

We find that 7803 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 172 = 289 , which gives 27 as quotient and we know that 27 is a perfect cube

(vi)
107811

Prime factors of 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11 = 33 × 113 × 3

We find that 107811 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 3, which gives 35937 as quotient and we know that 35937 is a perfect cube.

(vii) 35721

Prime factors of 35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 =
33 × 33 × 72

We find that 35721 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 72 = 49, which gives 729 as quotient and we know that 729 is a perfect cube

(viii) 243000

Prime factors of 243000 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 = 23 × 33 × 53 × 32

We find that 243000 is not a perfect cube.

Hence, for making the quotient a perfect cube we divide it by 32 = 9, which gives 27000 as quotient and we know that 27000 is a perfect cube

### What smallest number should 7803 be multiplied with so that the product becomes a perfect cube ?`?

Hence, `17` is the smallest number by which `7803` should be multiplied to make it a perfect cube.

### What is the smallest number by which 6912 must be divided to make it a perfect cube?

To do: To find the smallest number by which 6912 must be divided so that the number formed is a perfect cube. Therefore, we should divide 6912 by 22=4 2 2 = 4 , the smallest number to get 1728 which is a cube of 12 .

### What is the smallest number by which 10976 must be divided to make it a perfect cube?

Hence, the smallest number by which 10976 must be multiplied to obtain a perfect cube is 2.

### What is the smallest number with which 7803 must be divided so that the quotient is a perfect cube?

Hence, 7803 is not a perfect cube. We divide it by 172 = 289 to make the quotient a perfect cube, which gives 27 as quotient which is a perfect cube. Hence, 289 is the required smallest number.
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