Is 370 a prime number?

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

For 370, the answer is: No, 370 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 370) is as follows: 1, 2, 5, 10, 37, 74, 185, 370.

For 370 to be a prime number, it would have been required that 370 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 370 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 370 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

370 is a multiple of 1
370 is a multiple of 2
370 is a multiple of 5
370 is a multiple of 10
370 is a multiple of 37
370 is a multiple of 74
370 is a multiple of 185

For 370 to be a prime number, it would have been required that 370 has only two divisors, i.e., itself and 1.

Is 370 a deficient number?

Yes, 370 is a deficient number, that is to say 370 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 370 without 370 itself (that is 1 + 2 + 5 + 10 + 37 + 74 + 185 = 314).

Parity of 370

370 is an even number, because it is evenly divisible by 2: 370 / 2 = 185.

Find out more:

What is an even number?

Is 370 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 370 is about 19.235.

Thus, the square root of 370 is not an integer, and therefore 370 is not a square number.

What is the square number of 370?

The square of a number (here 370) is the result of the product of this number (370) by itself (i.e., 370 × 370); the square of 370 is sometimes called "raising 370 to the power 2", or "370 squared".

The square of 370 is 136 900 because 370 × 370 = 370² = 136 900.

As a consequence, 370 is the square root of 136 900.

Number of digits of 370

370 is a number with 3 digits.

What are the multiples of 370?

The multiples of 370 are all integers evenly divisible by 370, that is all numbers such that the remainder of the division by 370 is zero. There are infinitely many multiples of 370. The smallest multiples of 370 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 370 too, since 0 × 370 = 0
370: indeed, 370 is a multiple of itself, since 370 is evenly divisible by 370 (we have 370 / 370 = 1, so the remainder of this division is indeed zero)
740: indeed, 740 = 370 × 2
1 110: indeed, 1 110 = 370 × 3
1 480: indeed, 1 480 = 370 × 4
1 850: indeed, 1 850 = 370 × 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 370). 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 19.235). 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 370

Preceding numbers: …368, 369
Following numbers: 371, 372…

Nearest numbers from 370

Preceding prime number: 367
Following prime number: 373