Is 780 a prime number?

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

For 780, the answer is: No, 780 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 780) is as follows: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780.

For 780 to be a prime number, it would have been required that 780 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 780 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 780 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

780 is a multiple of 1
780 is a multiple of 2
780 is a multiple of 3
780 is a multiple of 4
780 is a multiple of 5
780 is a multiple of 6
780 is a multiple of 10
780 is a multiple of 12
780 is a multiple of 13
780 is a multiple of 15
780 is a multiple of 20
780 is a multiple of 26
780 is a multiple of 30
780 is a multiple of 39
780 is a multiple of 52
780 is a multiple of 60
780 is a multiple of 65
780 is a multiple of 78
780 is a multiple of 130
780 is a multiple of 156
780 is a multiple of 195
780 is a multiple of 260
780 is a multiple of 390

For 780 to be a prime number, it would have been required that 780 has only two divisors, i.e., itself and 1.

Is 780 a deficient number?

No, 780 is not a deficient number: to be deficient, 780 should have been such that 780 is larger than the sum of its proper divisors, i.e., the divisors of 780 without 780 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 13 + 15 + 20 + 26 + 30 + 39 + 52 + 60 + 65 + 78 + 130 + 156 + 195 + 260 + 390 = 1 572).

In fact, 780 is an abundant number; 780 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 13 + 15 + 20 + 26 + 30 + 39 + 52 + 60 + 65 + 78 + 130 + 156 + 195 + 260 + 390 = 1 572). The smallest abundant number is 12.

Parity of 780

780 is an even number, because it is evenly divisible by 2: 780 / 2 = 390.

Find out more:

What is an even number?

Is 780 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 780 is about 27.928.

Thus, the square root of 780 is not an integer, and therefore 780 is not a square number.

What is the square number of 780?

The square of a number (here 780) is the result of the product of this number (780) by itself (i.e., 780 × 780); the square of 780 is sometimes called "raising 780 to the power 2", or "780 squared".

The square of 780 is 608 400 because 780 × 780 = 780² = 608 400.

As a consequence, 780 is the square root of 608 400.

Number of digits of 780

780 is a number with 3 digits.

What are the multiples of 780?

The multiples of 780 are all integers evenly divisible by 780, that is all numbers such that the remainder of the division by 780 is zero. There are infinitely many multiples of 780. The smallest multiples of 780 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 780 too, since 0 × 780 = 0
780: indeed, 780 is a multiple of itself, since 780 is evenly divisible by 780 (we have 780 / 780 = 1, so the remainder of this division is indeed zero)
1 560: indeed, 1 560 = 780 × 2
2 340: indeed, 2 340 = 780 × 3
3 120: indeed, 3 120 = 780 × 4
3 900: indeed, 3 900 = 780 × 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 780). 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 27.928). 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 780

Preceding numbers: …778, 779
Following numbers: 781, 782…

Nearest numbers from 780

Preceding prime number: 773
Following prime number: 787