Is 272 a prime number?

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

For 272, the answer is: No, 272 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 272) is as follows: 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.

For 272 to be a prime number, it would have been required that 272 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

272 is a multiple of 1
272 is a multiple of 2
272 is a multiple of 4
272 is a multiple of 8
272 is a multiple of 16
272 is a multiple of 17
272 is a multiple of 34
272 is a multiple of 68
272 is a multiple of 136

For 272 to be a prime number, it would have been required that 272 has only two divisors, i.e., itself and 1.

Is 272 a deficient number?

No, 272 is not a deficient number: to be deficient, 272 should have been such that 272 is larger than the sum of its proper divisors, i.e., the divisors of 272 without 272 itself (that is 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 = 286).

In fact, 272 is an abundant number; 272 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 = 286). The smallest abundant number is 12.

Parity of 272

272 is an even number, because it is evenly divisible by 2: 272 / 2 = 136.

Find out more:

What is an even number?

Is 272 a perfect square 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 272 is about 16.492.

Thus, the square root of 272 is not an integer, and therefore 272 is not a square number.

What is the square number of 272?

The square of a number (here 272) is the result of the product of this number (272) by itself (i.e., 272 × 272); the square of 272 is sometimes called "raising 272 to the power 2", or "272 squared".

The square of 272 is 73 984 because 272 × 272 = 272² = 73 984.

As a consequence, 272 is the square root of 73 984.

Number of digits of 272

272 is a number with 3 digits.

What are the multiples of 272?

The multiples of 272 are all integers evenly divisible by 272, that is all numbers such that the remainder of the division by 272 is zero. There are infinitely many multiples of 272. The smallest multiples of 272 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 272 too, since 0 × 272 = 0
272: indeed, 272 is a multiple of itself, since 272 is evenly divisible by 272 (we have 272 / 272 = 1, so the remainder of this division is indeed zero)
544: indeed, 544 = 272 × 2
816: indeed, 816 = 272 × 3
1 088: indeed, 1 088 = 272 × 4
1 360: indeed, 1 360 = 272 × 5
etc.

How to determine whether an integer is a prime number?

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 272). 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 about 16.492). 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.

Numbers near 272

Preceding numbers: …270, 271
Following numbers: 273, 274…

Nearest numbers from 272

Preceding prime number: 271
Following prime number: 277