is 2311 a prime or composite number?
On my calculator I just tried for about 2 minutes to divide 2311 by primes < 49 (since 49^2 > 2311 , there is not need to go higher)
Actually the first few were pretty obvious, so I started with 7 , then
11,13,17,19,23,29,31,37,41,43,47
none divided exactly so, 2311 is prime
To determine if the number 2311 is prime or composite, we need to check if it is divisible by any numbers other than 1 and itself.
One way to do this is to divide 2311 by all the numbers from 2 up to the square root of 2311, rounded up to the nearest whole number. If any of these divisions result in an exact quotient, then 2311 is not prime and is instead composite.
Let's check:
The square root of 2311 is approximately 48.07013, rounding up to 49.
Now, we'll divide 2311 by all the numbers from 2 to 49:
2311 ÷ 2 = 1155.5 (not an exact quotient)
2311 ÷ 3 = 770.33 (not an exact quotient)
2311 ÷ 4 = 577.75 (not an exact quotient)
2311 ÷ 5 = 462.2 (not an exact quotient)
2311 ÷ 6 = 385.1667 (not an exact quotient)
2311 ÷ 7 = 330.1429 (not an exact quotient)
2311 ÷ 8 = 288.875 (not an exact quotient)
2311 ÷ 9 = 256.7778 (not an exact quotient)
2311 ÷ 10 = 231.1 (not an exact quotient)
...
2311 ÷ 48 = 48.14583 (not an exact quotient)
2311 ÷ 49 = 47.2459 (not an exact quotient)
After checking for divisibility by all the numbers from 2 to 49, we found that none of these divisions resulted in an exact quotient. Therefore, 2311 is a prime number.