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What is the greatest 3 digit number with only 3 and 5 (each repeated at least once)?

  • Last Updated : 17 Aug, 2021

In our daily lives, we use numbers. They are frequently referred to as numerals. We can’t count objects, date, time, money, or anything else without numbers. These numerals are sometimes used for measurement and other times for labeling. Numbers have features that allow them to conduct arithmetic operations on them. These figures are expressed both numerically and in words. For example, 3 is written as three, 33 is written as thirty-three, and so on. To learn further, students might practice writing the numbers from 1 to 100 in words.

There are various types of numbers that we learn in Math. Natural and whole numbers, odd and even numbers, rational and irrational numbers, and so on are all examples. In this article, we’ll go through all of the different varieties. Aside from that, the numbers are utilized in a variety of applications, including number series, arithmetic tables, and so on.

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  • A number is an arithmetic value that is used to represent and calculate a quantity. Numbers are represented by numerals, which are written symbols such as “2.”
  • A number system is a method of writing numbers that uses logical digits or symbols to represent them.

Types of Numbers

The number system is a system for categorizing numbers into sets. In math, there are several different types of numbers:



  • Natural Numbers: Natural numbers are positive integers from 1 to infinity that contain the positive integers 1 to infinity. The set of natural numbers is indicated by the letter “N,” and it consists of N = 1, 2, 3, 4, 5,…………
  • Whole Numbers: Non-negative integers, often known as whole numbers, are non-negative integers that do not contain any fractional or decimal parts. It is symbolized by the letter “W,” and the set of whole numbers contains W = 0, 1, 2, 3, 4, 5,…………
  • Integers: Integers are the set of all whole numbers, but they also include a set of negative natural numbers. Integers are represented by the letter “Z,” and the set of integers is Z = -3, -2, -1, 0, 1, 2, 3.
  • Real Numbers: Real numbers are all positive and negative integers, fractional and decimal numbers that do not contain imaginary values. The letter “R” is used to signify it.
  • Rational Numbers: Rational numbers are any numbers that may be expressed as a ratio of one number to another number. Any number that may be written in the form of p/q qualifies. The rational number is represented by the symbol “Q.”
  • Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a ratio of one to another and are denoted by the letter P.
  • Complex Numbers: Complex numbers (C) are numbers that may be expressed in the form a+bi, where “a” and “b” are real numbers and I is an imaginary number.

Places in a number: If a number is 12345 then 5 is at units place, 4 is at tens place, 3 is at hundredth place, 2 is at thousand place, and so on…….

So, a number can be written as : 
1*(Digit at ones place) + 10*(Digit at tens place) + 100*(Digit at hundreds place)+………………….

What is the greatest 3-digit number with only 3 and 5(each repeated at least once)?

Solution: 

Three-digit numbers start from 100, 101, 102,…………. to 999.

We have to find the number with digits only 3 and 5 so there can be cases like:

  • Use 3 and 5 both at least once.
  • Use only 3 and 5 

Case 1: As 999 is the largest three-digit number but we have to use 3 and 5 at-least once.
So, we can put 5 and 3 at tens and ones place respectively.
So, the number will be 953.
If we put 3 at tens place and 5 at ones place the number will be 935 which is smaller than 953.
So, 953 is the largest 3-digit number with 3 and 5 (using at-least once).

Case 2: As 999 is the largest three-digit number but we have to use 3 and 5 only. So, we can put 5 at hundred and tens place and 3 at units place. So, the number will be 553. 

Similar Questions

Question 1: What is the greatest 3-digit number with only 7 and 8?



Solution: 

Three-digit numbers start from 100, 101, 102,…………. to 999.
We have to find the number with digits only 7 and 8 so there can be cases like :

  • Use 7 and 8 both at least once.
  • Use only 7 and 8 (Both at-least once )

Case-1: As 999 is the largest three-digit number but we have to use 7 and 8 at-least once.So, we can put 8 and 7 at tens and ones place respectively. So, the number will be 987. 
If we put 7 at tens place and 8 at ones place the number will be 978 which is smaller than 987. 
So, 987 is the largest 3-digit number with 7 and 9 (using at-least once).

Case-2: As 999 is the largest three-digit number but we have to use 7 and 8 only. So, we can put 8 at hundred and tens place and 7 at units place. So, the number will be 887. 

Question 2: What is the greatest 2-digit number with only 1 and 9?

Solution: 

Two-digit numbers start from 10, 11, 12,…………. to 99.
We have to find the number with digits only 1 and 9 so there can be cases like :

  • Use 1 and 9 both at least once.
  • Use only 1 and 9

For 2-digits number, both cases are same:

As 99 is the largest two-digit number but we have to use 1 and 9 at-least once.So, we can put 9 and 1 at tens and ones place respectively. So, the number will be 91.
If we put 1 at tens place and 9 at ones place the number will be 19 which is smaller than 91. 
So, 91 is the largest 2-digit number with only 1 and 9 (using at-least once).

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