Is 36 A Prime Number?

Is 36 a prime number? What are the divisors of 36? To content

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 36, the answer is: No, 36 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 36) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 36.

For 36 to be a prime number, it would have been required that 36 has only two divisors, i.e., itself and 1.

Find out more:

• What is a prime number?

As a consequence:

• 36 is a multiple of 1
• 36 is a multiple of 2
• 36 is a multiple of 3
• 36 is a multiple of 4
• 36 is a multiple of 6
• 36 is a multiple of 9
• 36 is a multiple of 12
• 36 is a multiple of 18

For 36 to be a prime number, it would have been required that 36 has only two divisors, i.e., itself and 1.

Is 36 a deficient number?

No, 36 is not a deficient number: to be deficient, 36 should have been such that 36 is larger than the sum of its proper divisors, i.e., the divisors of 36 without 36 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55).

In fact, 36 is an abundant number; 36 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55). The smallest abundant number is 12.

36 is an even number, because it is evenly divisible by 2: 36 / 2 = 18.

Find out more:

• What is an even number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 36 is 6.

Therefore, the square root of 36 is an integer, and as a consequence 36 is a perfect square.

As a consequence, 6 is the square root of 36.

The square of a number (here 36) is the result of the product of this number (36) by itself (i.e., 36 × 36); the square of 36 is sometimes called "raising 36 to the power 2", or "36 squared".

The square of 36 is 1 296 because 36 × 36 = 362 = 1 296.

As a consequence, 36 is the square root of 1 296.

36 is a number with 2 digits.

The multiples of 36 are all integers evenly divisible by 36, that is all numbers such that the remainder of the division by 36 is zero. There are infinitely many multiples of 36. The smallest multiples of 36 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 36 too, since 0 × 36 = 0
• 36: indeed, 36 is a multiple of itself, since 36 is evenly divisible by 36 (we have 36 / 36 = 1, so the remainder of this division is indeed zero)
• 72: indeed, 72 = 36 × 2
• 108: indeed, 108 = 36 × 3
• 144: indeed, 144 = 36 × 4
• 180: indeed, 180 = 36 × 5
• etc.

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 36). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is 6). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

• Preceding numbers: …34, 35
• Following numbers: 37, 38…

Nearest numbers from 36

• Preceding prime number: 31
• Following prime number: 37

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• A list of prime numbers
• What is an even number?
• What is a multiple of 3?
• What is a multiple of 5?
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