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How many odd numbers are there between 1 and 10,000?

Published in Number Properties 2 mins read

There are exactly 5,000 odd numbers between 1 and 10,000.

Understanding Odd Numbers

An odd number is any integer that is not divisible by 2. When an odd number is divided by 2, it leaves a remainder of 1. Odd numbers always end with one of the following digits: 1, 3, 5, 7, or 9.

For example:

  • 1, 3, 5, 7, 9 are the first five odd numbers.
  • 101, 247, 9999 are also odd numbers.

Determining the Count of Odd Numbers in a Range

When counting numbers in a consecutive range starting from 1, odd and even numbers typically alternate. This means that, for a given range from 1 to a number 'N', approximately half of the numbers will be odd and half will be even.

Specifically:

  • If 'N' is an even number, the count of odd numbers from 1 to N is exactly N/2.
  • If 'N' is an odd number, the count of odd numbers from 1 to N is (N+1)/2.

In the case of the range from 1 to 10,000, since 10,000 is an even number, the count of odd numbers is 10,000 / 2 = 5,000.

Reference Data from Byju's

The information provided by Byju's directly supports this calculation, illustrating the pattern for various number ranges:

Number Range No. of Odd Numbers
1 to 300 150
1 to 500 250
1 to 1000 500
1 to 10000 5000

Source: Odd Numbers (Definition, Chart, Properties & Solved Examples) byjus.com

As the table clearly indicates, for the range from 1 to 10,000, there are 5,000 odd numbers.

Exact Answer

Based on the properties of odd numbers and confirmed by the provided reference, the exact number of odd integers between 1 and 10,000 (inclusive of 1, as it is an odd number, and considering the full range up to 10,000) is 5,000.