Identify the number 126 as either prime or composite. Show or explain why

All even numbers higher than 2 are composite, because 2 is the only even prime.

To determine if the number 126 is prime or composite, we need to check if it has any factors other than 1 and itself.

By dividing 126 by different numbers, we can find its factors:

126 ÷ 2 = 63
126 ÷ 3 = 42
126 ÷ 4 = 31.5 (not a whole number)
126 ÷ 5 = 25.2 (not a whole number)
126 ÷ 6 = 21
126 ÷ 7 = 18
126 ÷ 8 = 15.75 (not a whole number)
126 ÷ 9 = 14
126 ÷ 10 = 12.6 (not a whole number)

From the division above, we see that 126 has factors other than 1 and itself (2, 3, 6, 7, 9, 14, 18, 21, 42, 63). Therefore, 126 is a composite number, as it has factors other than just 1 and itself.

To determine whether the number 126 is prime or composite, we need to identify its factors. A prime number is a number that is divisible only by 1 and itself, whereas a composite number has at least one factor other than 1 and itself.

To find the factors of 126, we can start by dividing it by the smallest prime number, which is 2. If 126 is divisible by 2 without leaving a remainder, then 2 is a factor of 126. If not, we move on to the next prime number, which is 3, and continue the process until we have exhausted all possible numbers up to the square root of 126.

Let's follow this method:

1. Check if 126 is divisible by 2: 126 ÷ 2 = 63. Yes, it is divisible by 2, so 2 is a factor.

Now, we divide 63 by the next smallest prime number, which is still 2:

2. Check if 63 is divisible by 2: 63 ÷ 2 = 31.5. No, it is not divisible by 2.

Now, we move on to the next prime number, which is 3:

3. Check if 63 is divisible by 3: 63 ÷ 3 = 21. Yes, it is divisible by 3, so 3 is a factor.

Now, we divide 21 by 3 again:

4. Check if 21 is divisible by 3: 21 ÷ 3 = 7. Yes, it is divisible by 3, so 3 is also a factor.

Finally, we are left with 7, which is a prime number itself. Let's check if it divides evenly into 7:

5. Check if 7 is divisible by 7: 7 ÷ 7 = 1. Yes, it is divisible by 7.

So, the factors of 126 are 1, 2, 3, 3, 7, and 7.

Since 126 has factors other than 1 and itself, namely 2, 3, 3, 7, and 7, it is a composite number.