Question:
7 $\times$ 11 $\times$ 13 + 5 is
7 $\times$ 11 $\times$ 13 + 5 is
Show Hint
Any even number ending in 0, 2, 4, 6, or 8 (except 2 itself) is always a composite number because it is divisible by 2.
This allows you to quickly eliminate prime and odd options without finding all factors.
This allows you to quickly eliminate prime and odd options without finding all factors.
Updated On: Jun 25, 2026
- a prime number.
- an odd number.
- a composite number.
- a multiple of 5.
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The question asks us to classify the number given by the expression \(7 \times 11 \times 13 + 5\) into one of the given categories: prime number, odd number, composite number, or a multiple of 5.
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
A composite number has more than two factors.
An odd number is not divisible by 2.
A multiple of 5 is divisible by 5.
Step 2: Key Formula or Approach:
We can simplify the expression arithmetically to find its exact integer value, or we can use factorization properties.
Simplifying the expression: \[ N = 7 \times 11 \times 13 + 5 \] Alternatively, we can factor out common terms to determine its divisibility.
Step 3: Detailed Explanation:
1. Let us first calculate the value of the given expression:
First, multiply the three numbers: \[ 7 \times 11 = 77 \] Now multiply 77 by 13: \[ 77 \times 13 = 1001 \] 2. Now, add 5 to the product: \[ N = 1001 + 5 = 1006 \] 3. Let us analyze the number 1006:
- Since 1006 is an even number (it ends in 6), it is divisible by 2.
- Because it has divisors other than 1 and itself (specifically, 1, 2, 503, and 1006), it is not a prime number.
- Since it is divisible by 2, it is an even number, so it is not an odd number.
- Since it does not end in 0 or 5, it is not a multiple of 5.
- Therefore, since it has more than two factors, it is a composite number.
Step 4: Final Answer:
The simplified value of the expression is 1006, which is an even number greater than 2 and thus a composite number.
Hence, the correct option is (C).
The question asks us to classify the number given by the expression \(7 \times 11 \times 13 + 5\) into one of the given categories: prime number, odd number, composite number, or a multiple of 5.
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
A composite number has more than two factors.
An odd number is not divisible by 2.
A multiple of 5 is divisible by 5.
Step 2: Key Formula or Approach:
We can simplify the expression arithmetically to find its exact integer value, or we can use factorization properties.
Simplifying the expression: \[ N = 7 \times 11 \times 13 + 5 \] Alternatively, we can factor out common terms to determine its divisibility.
Step 3: Detailed Explanation:
1. Let us first calculate the value of the given expression:
First, multiply the three numbers: \[ 7 \times 11 = 77 \] Now multiply 77 by 13: \[ 77 \times 13 = 1001 \] 2. Now, add 5 to the product: \[ N = 1001 + 5 = 1006 \] 3. Let us analyze the number 1006:
- Since 1006 is an even number (it ends in 6), it is divisible by 2.
- Because it has divisors other than 1 and itself (specifically, 1, 2, 503, and 1006), it is not a prime number.
- Since it is divisible by 2, it is an even number, so it is not an odd number.
- Since it does not end in 0 or 5, it is not a multiple of 5.
- Therefore, since it has more than two factors, it is a composite number.
Step 4: Final Answer:
The simplified value of the expression is 1006, which is an even number greater than 2 and thus a composite number.
Hence, the correct option is (C).
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