Question

the product of five different natural numbers is 2000 the difference between smallest and largest number is​

Answer 1

Answer:

v฿฿ⱬⱬ₦ⱬ₥

Step-by-step explanation:

₦₳₦₥₵ đj ₥₳ ₴₥ ₥₥₴ ₦J₵ ฿₥₵ ₴฿ ฿฿₵

Answer 2

The difference between the smallest and largest number is 24.

Condition Given:

The product of five different natural numbers is 2000.

To Find:

The difference between the largest and smallest number =?

Solution:

Here, when we find all the prime factors of the number 2000, we get;

2000 = $2^{4}$ × $5^{3}$

i.e.,  2000 = 2 × 2 × 2 × 2 × 5 × 5 × 5

Now, we need a combination of 5 different numbers as mentioned in the question.

We know, that the smallest number we can take is '1'.

But, to calculate the largest number so that a group of five different numbers could be formed is;

2000 = (2) × (2 × 2 × 2) × (5) × (5 × 5)

i.e., 2000 = (2) × (8) × (5) × (25)

From here, we can see that the greatest number possible for all five numbers to be distinct is '25'.

∴ Greatest Number - smallest Number = 25 - 1

∴ Difference = 24

Thus, the difference between the largest and smallest number is 24.

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