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Is 91 a prime number?

Is 91 a prime number?

Before moving to find whether 91 is a prime number or not, let us see what prime numbers are. Prime numbers are those numbers that are divisible by only two numbers, 1 and itself. On the other hand, composite numbers are those numbers that are divisible by their factors, 1 and the number itself.

Coming back to the question, whether 91 is a prime number or not, the answer is- it is not! 91 is a composite number that can be factored into different numbers. Let us find the factors of 91 by the most straightforward method, prime factorisation.

91 = 7 x 13

Since 91 is divisible by 1, 7, 13 and 91, it cannot be kept under prime numbers. Instead, it has to be kept under composite numbers.

What is 91, then?

Indeed, 91 does not fall in the category of prime numbers. It can instead be put in the category of these numbers: -

  • Natural numbers
  • Composite numbers
  • Whole numbers
  • Positive integers
  • Odd numbers

Answers of some questions about 91

Is 91 a Prime Number? No
Is 91 a Composite Number? Yes
What is the square of 91? 8281
Does 91 have a perfect cube? No
Square Root of 91 9.539392
Is 91 an Odd Number? Yes
Is 91 an Even Number? No
Is 91 a Perfect Square? No
What is the cube root of 91? 4.497935

Shortcut method to find whether 91 is a prime number or not

Firstly, we need to check the divisibility of (9+1) by 3 to find whether 91 is a prime number or not. Since 9+1 is 10 and not divisible by 3, we have to continue with the following steps.

Step 1: Find the square root of 91 in the first place, i.e. √91 = 9.53

Step 2: Now, choose the prime numbers less than 9 and find numbers dividing 91 into two halves.

Step 3: After doing divisions, we get to know that 91 is divisible by 7 completely. Hence, it is not a prime number.

One can use this technique to check the prime number property of various numbers.

Facts about 91

  1. It is spelled ninety-one. One of the common mistakes everyone makes is they spell ninety as ninty.
  2. 91 is the 27th distinct semiprime number and stands second of the form (7xq).
  3. 91 is a triangular and hexagonal number. 91 is special to be called a centred hexagonal number.
  4. It is a centred nonagonal number, a centred cube number and a square pyramidal number.
  5. 91 is the smallest positive integer that can be expressed as two cubes in two different ways (conditioned negative numbers are also allowed). 91 = 63 + (−5)3 = 43 + 33
  6. 91 is the smallest positive integer expressible as a sum of six distinct squares. 91 = 12 + 22 + 32 + 42 + 52 + 62
  7. 91 is the smallest pseudoprime satisfying the congruence 3n ≡ 3 mod n.
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