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 ⇢ 9999
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,
- Decimal Number System
- Binary Number System
- Octal Number System
- 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 × 163 + 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
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...