Is 378 a prime number?

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

For 378, the answer is: No, 378 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 378) is as follows: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.

For 378 to be a prime number, it would have been required that 378 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

378 is a multiple of 1
378 is a multiple of 2
378 is a multiple of 3
378 is a multiple of 6
378 is a multiple of 7
378 is a multiple of 9
378 is a multiple of 14
378 is a multiple of 18
378 is a multiple of 21
378 is a multiple of 27
378 is a multiple of 42
378 is a multiple of 54
378 is a multiple of 63
378 is a multiple of 126
378 is a multiple of 189

For 378 to be a prime number, it would have been required that 378 has only two divisors, i.e., itself and 1.

Is 378 a deficient number?

No, 378 is not a deficient number: to be deficient, 378 should have been such that 378 is larger than the sum of its proper divisors, i.e., the divisors of 378 without 378 itself (that is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 27 + 42 + 54 + 63 + 126 + 189 = 582).

In fact, 378 is an abundant number; 378 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 27 + 42 + 54 + 63 + 126 + 189 = 582). The smallest abundant number is 12.

Parity of 378

378 is an even number, because it is evenly divisible by 2: 378 / 2 = 189.

Find out more:

What is an even number?

Is 378 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 378 is about 19.442.

Thus, the square root of 378 is not an integer, and therefore 378 is not a square number.

What is the square number of 378?

The square of a number (here 378) is the result of the product of this number (378) by itself (i.e., 378 × 378); the square of 378 is sometimes called "raising 378 to the power 2", or "378 squared".

The square of 378 is 142 884 because 378 × 378 = 378² = 142 884.

As a consequence, 378 is the square root of 142 884.

Number of digits of 378

378 is a number with 3 digits.

What are the multiples of 378?

The multiples of 378 are all integers evenly divisible by 378, that is all numbers such that the remainder of the division by 378 is zero. There are infinitely many multiples of 378. The smallest multiples of 378 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 378 too, since 0 × 378 = 0
378: indeed, 378 is a multiple of itself, since 378 is evenly divisible by 378 (we have 378 / 378 = 1, so the remainder of this division is indeed zero)
756: indeed, 756 = 378 × 2
1 134: indeed, 1 134 = 378 × 3
1 512: indeed, 1 512 = 378 × 4
1 890: indeed, 1 890 = 378 × 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 378). 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 19.442). 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 378

Preceding numbers: …376, 377
Following numbers: 379, 380…

Nearest numbers from 378

Preceding prime number: 373
Following prime number: 379