Is 770 a prime number?

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

For 770, the answer is: No, 770 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 770) is as follows: 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770.

For 770 to be a prime number, it would have been required that 770 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 770 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 770 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

770 is a multiple of 1
770 is a multiple of 2
770 is a multiple of 5
770 is a multiple of 7
770 is a multiple of 10
770 is a multiple of 11
770 is a multiple of 14
770 is a multiple of 22
770 is a multiple of 35
770 is a multiple of 55
770 is a multiple of 70
770 is a multiple of 77
770 is a multiple of 110
770 is a multiple of 154
770 is a multiple of 385

For 770 to be a prime number, it would have been required that 770 has only two divisors, i.e., itself and 1.

Is 770 a deficient number?

No, 770 is not a deficient number: to be deficient, 770 should have been such that 770 is larger than the sum of its proper divisors, i.e., the divisors of 770 without 770 itself (that is 1 + 2 + 5 + 7 + 10 + 11 + 14 + 22 + 35 + 55 + 70 + 77 + 110 + 154 + 385 = 958).

In fact, 770 is an abundant number; 770 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 5 + 7 + 10 + 11 + 14 + 22 + 35 + 55 + 70 + 77 + 110 + 154 + 385 = 958). The smallest abundant number is 12.

Parity of 770

770 is an even number, because it is evenly divisible by 2: 770 / 2 = 385.

Find out more:

What is an even number?

Is 770 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 770 is about 27.749.

Thus, the square root of 770 is not an integer, and therefore 770 is not a square number.

What is the square number of 770?

The square of a number (here 770) is the result of the product of this number (770) by itself (i.e., 770 × 770); the square of 770 is sometimes called "raising 770 to the power 2", or "770 squared".

The square of 770 is 592 900 because 770 × 770 = 770² = 592 900.

As a consequence, 770 is the square root of 592 900.

Number of digits of 770

770 is a number with 3 digits.

What are the multiples of 770?

The multiples of 770 are all integers evenly divisible by 770, that is all numbers such that the remainder of the division by 770 is zero. There are infinitely many multiples of 770. The smallest multiples of 770 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 770 too, since 0 × 770 = 0
770: indeed, 770 is a multiple of itself, since 770 is evenly divisible by 770 (we have 770 / 770 = 1, so the remainder of this division is indeed zero)
1 540: indeed, 1 540 = 770 × 2
2 310: indeed, 2 310 = 770 × 3
3 080: indeed, 3 080 = 770 × 4
3 850: indeed, 3 850 = 770 × 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 770). 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 27.749). 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 770

Preceding numbers: …768, 769
Following numbers: 771, 772…

Nearest numbers from 770

Preceding prime number: 769
Following prime number: 773