What do we call the numbers that cannot be arranged into 2-row arrays?
The numbers that cannot be arranged into 2-row arrays are called prime numbers. Prime numbers are positive integers greater than 1 that have no divisors other than 1 and themselves.
To identify prime numbers, you can follow these steps:
1. Take the number you want to check.
2. Divide it by all the numbers from 2 up to the square root of that number.
3. If any of these divisions result in an even quotient (with no remainder), then the number is not prime.
4. If none of the divisions have an even quotient (indicate there is a remainder for all divisions), then the number is prime.
For example, let's check if the number 13 is prime:
1. Divide 13 by all the numbers from 2 up to the square root of 13 (approximately 3.61).
2. 13 ÷ 2 = 6.5 (not a whole number)
3. 13 ÷ 3 = 4.333 (not a whole number)
4. There are no other numbers less than or equal to the square root of 13 to check.
5. Since none of the divisions result in an even quotient, 13 is prime.
Prime numbers cannot be arranged into 2-row arrays because the requirement for a 2-row array is to have pairs of elements, which is not possible with prime numbers since they have no proper factors other than 1 and themselves.