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The number 3 × 5 × 7 × 11 + a, where a is the odd number is: a) Always prime number b) Always even number   c) Always odd number d) Composite number

The number 3 × 5 × 7 × 11 + a, where a is the odd number is: a) Always prime number b) Always even number   c) Always odd number d) Composite number Correct Answer b & d

Concept used:

Prime number: It is the positive integer having only two factors, 1 and itself.

Even number: A number that is divisible by 2

Odd number: A number that is not divisible by 2 

Composite number: The composite number is the positive integers which have more than two factors.

Calculation:

Our number is 3 × 5 × 7 × 11 + a

Taking a = 1, then

Number = 1155 + 1 = 1156

Taking a = 3, then

Number = 1155 + 3 = 1158

∴ The given number is a composite number and always even number.

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