Is 948 a prime number?

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

For 948, the answer is: No, 948 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 948) is as follows: 1, 2, 3, 4, 6, 12, 79, 158, 237, 316, 474, 948.

For 948 to be a prime number, it would have been required that 948 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

948 is a multiple of 1
948 is a multiple of 2
948 is a multiple of 3
948 is a multiple of 4
948 is a multiple of 6
948 is a multiple of 12
948 is a multiple of 79
948 is a multiple of 158
948 is a multiple of 237
948 is a multiple of 316
948 is a multiple of 474

For 948 to be a prime number, it would have been required that 948 has only two divisors, i.e., itself and 1.

Is 948 a deficient number?

No, 948 is not a deficient number: to be deficient, 948 should have been such that 948 is larger than the sum of its proper divisors, i.e., the divisors of 948 without 948 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 79 + 158 + 237 + 316 + 474 = 1 292).

In fact, 948 is an abundant number; 948 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 79 + 158 + 237 + 316 + 474 = 1 292). The smallest abundant number is 12.

Parity of 948

948 is an even number, because it is evenly divisible by 2: 948 / 2 = 474.

Find out more:

What is an even number?

Is 948 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 948 is about 30.790.

Thus, the square root of 948 is not an integer, and therefore 948 is not a square number.

What is the square number of 948?

The square of a number (here 948) is the result of the product of this number (948) by itself (i.e., 948 × 948); the square of 948 is sometimes called "raising 948 to the power 2", or "948 squared".

The square of 948 is 898 704 because 948 × 948 = 948² = 898 704.

As a consequence, 948 is the square root of 898 704.

Number of digits of 948

948 is a number with 3 digits.

What are the multiples of 948?

The multiples of 948 are all integers evenly divisible by 948, that is all numbers such that the remainder of the division by 948 is zero. There are infinitely many multiples of 948. The smallest multiples of 948 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 948 too, since 0 × 948 = 0
948: indeed, 948 is a multiple of itself, since 948 is evenly divisible by 948 (we have 948 / 948 = 1, so the remainder of this division is indeed zero)
1 896: indeed, 1 896 = 948 × 2
2 844: indeed, 2 844 = 948 × 3
3 792: indeed, 3 792 = 948 × 4
4 740: indeed, 4 740 = 948 × 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 948). 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 30.790). 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 948

Preceding numbers: …946, 947
Following numbers: 949, 950…

Nearest numbers from 948

Preceding prime number: 947
Following prime number: 953