Is 474 a prime number?

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

For 474, the answer is: No, 474 is not a prime number.

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

For 474 to be a prime number, it would have been required that 474 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

474 is a multiple of 1
474 is a multiple of 2
474 is a multiple of 3
474 is a multiple of 6
474 is a multiple of 79
474 is a multiple of 158
474 is a multiple of 237

For 474 to be a prime number, it would have been required that 474 has only two divisors, i.e., itself and 1.

Is 474 a deficient number?

No, 474 is not a deficient number: to be deficient, 474 should have been such that 474 is larger than the sum of its proper divisors, i.e., the divisors of 474 without 474 itself (that is 1 + 2 + 3 + 6 + 79 + 158 + 237 = 486).

In fact, 474 is an abundant number; 474 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 79 + 158 + 237 = 486). The smallest abundant number is 12.

Parity of 474

474 is an even number, because it is evenly divisible by 2: 474 / 2 = 237.

Find out more:

What is an even number?

Is 474 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 474 is about 21.772.

Thus, the square root of 474 is not an integer, and therefore 474 is not a square number.

What is the square number of 474?

The square of a number (here 474) is the result of the product of this number (474) by itself (i.e., 474 × 474); the square of 474 is sometimes called "raising 474 to the power 2", or "474 squared".

The square of 474 is 224 676 because 474 × 474 = 474² = 224 676.

As a consequence, 474 is the square root of 224 676.

Number of digits of 474

474 is a number with 3 digits.

What are the multiples of 474?

The multiples of 474 are all integers evenly divisible by 474, that is all numbers such that the remainder of the division by 474 is zero. There are infinitely many multiples of 474. The smallest multiples of 474 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 474 too, since 0 × 474 = 0
474: indeed, 474 is a multiple of itself, since 474 is evenly divisible by 474 (we have 474 / 474 = 1, so the remainder of this division is indeed zero)
948: indeed, 948 = 474 × 2
1 422: indeed, 1 422 = 474 × 3
1 896: indeed, 1 896 = 474 × 4
2 370: indeed, 2 370 = 474 × 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 474). 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 21.772). 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 474

Preceding numbers: …472, 473
Following numbers: 475, 476…

Nearest numbers from 474

Preceding prime number: 467
Following prime number: 479