To find the value of the given expression \( 5 \times 11 \times 17 + 3 \times 11 \) and determine its nature, let's break it down and compute each part step by step.
1. First part of the expression:
[tex]\[
5 \times 11 \times 17
\][/tex]
Compute this multiplication:
[tex]\[
5 \times 11 = 55
\][/tex]
Then,
[tex]\[
55 \times 17 = 935
\][/tex]
2. Second part of the expression:
[tex]\[
3 \times 11
\][/tex]
Compute this multiplication:
[tex]\[
3 \times 11 = 33
\][/tex]
3. Sum the results of the two parts to get the final result:
[tex]\[
935 + 33
\][/tex]
Compute this addition:
[tex]\[
935 + 33 = 968
\][/tex]
Now that we have the value of the expression, \( 968 \), we need to determine its nature. Specifically, we want to decide if it is a composite number.
A composite number is a positive integer greater than 1 that has more than two positive divisors. In simpler terms, it should have factors other than 1 and itself.
To check if 968 is a composite number:
- We see that 968 is even (it ends in 8), so it is divisible by 2.
- Dividing by 2:
[tex]\[
968 \div 2 = 484
\][/tex]
- This confirms that 968 has divisors other than 1 and 968 itself.
Hence, the number 968 is indeed a composite number. Therefore, [tex]\( 5 \times 11 \times 17 + 3 \times 11 \)[/tex] is a composite number.
