Is 760 a prime number?

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

For 760, the answer is: No, 760 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 760) is as follows: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760.

For 760 to be a prime number, it would have been required that 760 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 760 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 760 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

760 is a multiple of 1
760 is a multiple of 2
760 is a multiple of 4
760 is a multiple of 5
760 is a multiple of 8
760 is a multiple of 10
760 is a multiple of 19
760 is a multiple of 20
760 is a multiple of 38
760 is a multiple of 40
760 is a multiple of 76
760 is a multiple of 95
760 is a multiple of 152
760 is a multiple of 190
760 is a multiple of 380

For 760 to be a prime number, it would have been required that 760 has only two divisors, i.e., itself and 1.

Is 760 a deficient number?

No, 760 is not a deficient number: to be deficient, 760 should have been such that 760 is larger than the sum of its proper divisors, i.e., the divisors of 760 without 760 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 19 + 20 + 38 + 40 + 76 + 95 + 152 + 190 + 380 = 1 040).

In fact, 760 is an abundant number; 760 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 19 + 20 + 38 + 40 + 76 + 95 + 152 + 190 + 380 = 1 040). The smallest abundant number is 12.

Parity of 760

760 is an even number, because it is evenly divisible by 2: 760 / 2 = 380.

Find out more:

What is an even number?

Is 760 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 760 is about 27.568.

Thus, the square root of 760 is not an integer, and therefore 760 is not a square number.

What is the square number of 760?

The square of a number (here 760) is the result of the product of this number (760) by itself (i.e., 760 × 760); the square of 760 is sometimes called "raising 760 to the power 2", or "760 squared".

The square of 760 is 577 600 because 760 × 760 = 760² = 577 600.

As a consequence, 760 is the square root of 577 600.

Number of digits of 760

760 is a number with 3 digits.

What are the multiples of 760?

The multiples of 760 are all integers evenly divisible by 760, that is all numbers such that the remainder of the division by 760 is zero. There are infinitely many multiples of 760. The smallest multiples of 760 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 760 too, since 0 × 760 = 0
760: indeed, 760 is a multiple of itself, since 760 is evenly divisible by 760 (we have 760 / 760 = 1, so the remainder of this division is indeed zero)
1 520: indeed, 1 520 = 760 × 2
2 280: indeed, 2 280 = 760 × 3
3 040: indeed, 3 040 = 760 × 4
3 800: indeed, 3 800 = 760 × 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 760). 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 27.568). 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 760

Preceding numbers: …758, 759
Following numbers: 761, 762…

Nearest numbers from 760

Preceding prime number: 757
Following prime number: 761