Question

Find the largest cube number less than 2000

Answer 1

The largest cube number less than 2000 is 1000

Given:

Number 2000

To find:

Find the largest cube number less than 2000

Solutions:

A perfect cube number is a number which can be written in the form of a³

Example: 8 = 2³, 27 = 3³  

To find the largest cube number less than 2000

write 2000 as product of its prime factors

2000 = 2 × 2 × 2 × 2 × 5 × 5 × 5

Now group the above factors as triplets

2 × 2 × 2 × 2 × 5 × 5 × 5 = (2×2×2)× 2 × (5×5×5) = 2³ 5³ 2

Here one two is left alone

We need a number which a largest cube but less than 2000

So Remove 2

The cube number = 2³ 5³ = 1000.

The largest cube number less than 2000 is 1000

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Answer 2

Answer:

The answer to the given question is largest cube number less than 2000 is 1000.

Step-by-step explanation:

Given :

A number is given as 2000.

To find:

we have to find the largest cube number less than 2000.

Solution :

The problem is solved by a prime factorisation method.

The cube number is obtained by multiplying the number by itself two times.

A perfect cube number is a number that can be written as x³.

we have to find the factors of 2000 by the prime factorisation method.

$2)2000 \\ 2)1000 \\ 2)500 \\ 5)250 \\ 5)50 \\ 5)10 \\2)2 \\ )1$

The prime factors of the given number are 2*2*2*2*5*5*5

joining the factors as a triplet, we get the answers as

${2}^{3} \times {5}^{3} \times 2$

only one 2 is left with the power 1.

on ignoring the extra number, we get the value as

${2}^{3} \times {5}^{3}$

The value obtained is

$(8)(125) = 1000$

Therefore, the final answer to the given question is 1000.

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