## 12 Questions

What is the Roman numeral representation of 4000?

MMMCD

How many 'C' units make up 400?

4

What is the significance of the number 4000 in finance?

Represents a substantial amount of money

Which of the following is NOT a context where the number 4000 is significant?

History

How many 'M' units are used to represent 4000 in Roman numerals?

4

If the Roman numeral representation of 100 is 'C,' what would be the representation for 2000?

MM

How many factors does the number 4000 have?

7

What is the prime factorization of 4000?

$2^7 * 5^2$

Which of the following is NOT a factor of 4000?

100

How many multiples does the number 4000 have?

15

Which Roman numeral represents the number 4000?

MMMM

What is the product of two factors that produce 4000?

$10 * 400$

## Study Notes

## Number 4000: Exploring Factors, Multiples, and Roman Numerals

Number 4000 is a substantial figure, and understanding its characteristics, factors, multiples, and representation in Roman numerals can provide valuable insights into the world of mathematics and ancient history.

### Factors and Multiples

Number 4000 has seven *factors* (numbers that can be multiplied together to produce it) and fifteen *multiples* (the product of multiplying a factor by an integer).

Factors:

- 1
- 2
- 4
- 8 10 20 40

Multiples: 1 2 3 ... 3999 4000 4001 ...

The factors and multiples of 4000 are derived from its prime factorization: 2^7 * 5^2.

### Factor Pairs and Prime Factorization

The factors of 4000 are pairs of numbers that produce 4000 when multiplied together. For instance:

- 1 * 4000 = 4000
- 2 * 2000 = 4000
- 4 * 1000 = 4000
- 8 * 500 = 4000

These pairs, along with other factor combinations, lead to the prime factorization of 4000.

### Roman Numerals

Representing the number 4000 in Roman numerals is relatively straightforward. The largest unit in Roman numerals is 1000, known as "M," and there are 4000 of these. The next largest unit is 100, known as "C," and there are 4 "C" units, so we write 4 "C" as "CD."

The Roman numeral representation of 4000 is:

M M M M | C D |
---|---|

1000 | 100 |

This combination is read as "4000" in Roman numerals, "MMMCD."

### Applications and Considerations

The number 4000 is significant in various contexts, such as in time, measurement, and finance:

- Seconds: 4000 seconds is equivalent to approximately 66 minutes and 40 seconds.
- Miles: 4000 miles is a distance often seen on road signs as "4000 miles" or "4,000 miles."
- Currency: 4000 units of a particular currency represent a substantial amount of money.

Understanding the properties and representations of numbers like 4000 can help us grasp more complex mathematical concepts and expand our knowledge of history. The number 4000 serves as a stepping stone in a student's mathematical journey and a tangible example of how Roman numerals were used in antiquity.

In summary, 4000 is an intriguing number to examine for its factors and multiples and its representation in Roman numerals, shedding light on the fundamentals of mathematics and the historical significance of Roman numerals.

Explore the factors, multiples, and Roman numeral representation of the number 4000. Learn about its prime factorization, factor pairs, and how to convert 4000 into Roman numerals. Discover the applications and significance of the number 4000 in various contexts.

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