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What is the Greatest 4 Digit Number

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9999 is the greatest 4 Digit Number. To find the greatest 4-digit number, we need to maximize the value of each digit .9 is the highest value a single digit can have. So, the largest 4-digit number is formed by placing the digit ‘9’ in each of the four places: thousands, hundreds, tens, and ones.

In this article, we are going to find the largest 4-digit number, how to express it in terms of its prime factors and its properties, and different types of number systems.

What is the Greatest 4-digit number?

Greatest four-digit number can be expressed as the number with a digit at ones place, tenth place, hundredth place, and thousand place. All the digits have been the largest digits, in essence, 9. The largest four-digit number in the number system is ʉࢠ9999

Explanation: If 1 is added to this number, it becomes 10000 which is a five-digit number. So 9999 is the greatest four-digit number in the number system.

Largest four digit number in the number system = 9999

= 9999 + 1 

= 10000 (which is five digit number )

Hence it is proved that 9999 is the greatest four-digit number.

By this method, it is easy to find any greatest number in the number system.

Greatest 4-digit number as prime factors

Let’s express the largest 4-digit number in terms of its prime factors.

We are using the concept of prime numbers and prime factorisation to solve this.

Greatest 4-digit number is 9999.

9999 = 3 × 3 × 11 × 101

Thus, prime factors of the greatest 4-digit number 9999 are 3, 3, 11, 101.

Note: Prime factors are the factors of the given number which are prime.

Largest 4 Digit No Divisible by 15, 20 and 30

To find the largest 4-digit number divisible by 15, 20, and 30, we first need to determine the Least Common Multiple (LCM) of these numbers. The number we are looking for must be a multiple of this LCM.

Prime factorization of the numbers is,

15 = 3 × 5

20 = 2² × 5

30 = 2 × 3 × 5

LCM is the product of the highest power of each prime number present in the factorizations:

LCM (15, 20, 30) = 2² × 3 × 5 = 4 × 3 × 5 = 60

Now, we need to find the largest 4-digit number that is a multiple of 60.

Since 10000 is the smallest 5-digit number, the largest 4-digit number will be the largest multiple of 60 that is less than 10000.

To find this, we divide 10000 by 60 and round down to the nearest whole number:

10000/60 ≈ 166.7 ≈ 166.67

Rounding down gives us 166.

Now, we multiply 166 by 60 to find the largest 4-digit number that is divisible by 15, 20, and 30:

166×60 = 9960

166×60 =9960

Therefore, the largest 4-digit number divisible by 15, 20, and 30 is 9960.

Largest 4 digit number using different digits

If we use different digits to get the largest 4 digit number, we will come up with different numbers.

  • Greatest four-digit number, using only one digit is 9,999.
  • Greatest four-digit number, using two different digits is 9,998.
  • Greatest four-digit number, using all different digits is 9,876.

Number System in Maths- Types

The number system can exist for any base and it can have those number of digits involved accordingly.

Some important types of number system are as follows, 

  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System

Let’s see about all these types of number system in detail.

Decimal Number System 

Decimal number system consists of ten digits i.e. from 0 to 9. The base of a decimal number system is 10.

  • These digits can be used to represent or express any numeric value.
  • For example, the decimal number 153 consists of the digit 3 in one place, the digit 5 in the tens place, and the digit 1 in hundreds place which can be represented as, 

= (1×102) + (5×101) + (3×100)

= (1× 100) + (5× 10) + (3× 1), {where, 100 = 1}

= 100 + 50 + 3

= 153

Binary Number System 

Binary number system consists of only two digits i.e. 0 and 1. The base of the binary number system is 2.

  • The digital computer represents all kinds of data in a binary number system.
  • For example, convert 100112 into a decimal number system.

(100111)2 = 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20 

(100111)2 = 32 + 0 + 0 + 4 + 2 + 1

(100111)2 = (39)10

Octal Number System 

The octal number system consists of digits from 0 to 7. The base of the octal number system is 8.

  • Octal number systems are basically used in computer applications. For example, convert 1458 into decimal.

(1458)10 = 1 × 82 + 4 × 81+ 5 × 80 = 64 + 32 + 5 = (10110)8

Hexadecimal Number System

In hexadecimal number system, numbers are first represented from digits 0 to 9 as decimal number system and then the numbers are represented using alphabets from A to F.

  • The base of the hexadecimal number system is 16. For example, convert (26BC)16 to decimal.

(26BC)16 = 2 × 16+ 6 × 162 + 11 × 161 + 12 × 160

= 8192 + 1536 + 176 + 12

= 991610

Read More on Types of Number Systems

Conclusion- Largest 4 Digit Number

9999 is the largest 4 Digit Number. This article discussed the largest numbers in the 4 digits range in mathematics, how to express it in terms of its prime factors and its properties.

Read More,

Largest Four Digit Number- FAQs

1. What is the largest 4 digit even number?

9998 is the largest 4 digit even number.

2. What is the largest 4 digit number + 1 ?

The largest 4 digit number +1 is 10000.

3. What is the greatest 4 digit number that is a perfect square?

The greatest 4-digit number that is a perfect square is 9801.

4. What is the largest 4-digit number using the digits 0,3,4 1?

The greatest 4-digit number using the digits 0,3,4 is 4310.

5. What is the largest 4 digit number which is divisible by 15, 20 and 30?

The largest 4-digit number which is divisible by 15, 20, and 30 is 9960.

6. What is the largest 4 digit number?

The greatest 4 digit number in the number system is 9999.

7. What is the greatest 5 digit number?

The greatest 5 digit number in the number system is 99999.

8. What is the smallest 4 digit number?

The smallest 4-digit number is 1000.



Last Updated : 19 Dec, 2023
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