Is 429 a prime number?

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

For 429, the answer is: No, 429 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 429) is as follows: 1, 3, 11, 13, 33, 39, 143, 429.

For 429 to be a prime number, it would have been required that 429 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

429 is a multiple of 1
429 is a multiple of 3
429 is a multiple of 11
429 is a multiple of 13
429 is a multiple of 33
429 is a multiple of 39
429 is a multiple of 143

For 429 to be a prime number, it would have been required that 429 has only two divisors, i.e., itself and 1.

Is 429 a deficient number?

Yes, 429 is a deficient number, that is to say 429 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 429 without 429 itself (that is 1 + 3 + 11 + 13 + 33 + 39 + 143 = 243).

Parity of 429

429 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 429 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 429 is about 20.712.

Thus, the square root of 429 is not an integer, and therefore 429 is not a square number.

What is the square number of 429?

The square of a number (here 429) is the result of the product of this number (429) by itself (i.e., 429 × 429); the square of 429 is sometimes called "raising 429 to the power 2", or "429 squared".

The square of 429 is 184 041 because 429 × 429 = 429² = 184 041.

As a consequence, 429 is the square root of 184 041.

Number of digits of 429

429 is a number with 3 digits.

What are the multiples of 429?

The multiples of 429 are all integers evenly divisible by 429, that is all numbers such that the remainder of the division by 429 is zero. There are infinitely many multiples of 429. The smallest multiples of 429 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 429 too, since 0 × 429 = 0
429: indeed, 429 is a multiple of itself, since 429 is evenly divisible by 429 (we have 429 / 429 = 1, so the remainder of this division is indeed zero)
858: indeed, 858 = 429 × 2
1 287: indeed, 1 287 = 429 × 3
1 716: indeed, 1 716 = 429 × 4
2 145: indeed, 2 145 = 429 × 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 429). 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 20.712). 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 429

Preceding numbers: …427, 428
Following numbers: 430, 431…

Nearest numbers from 429

Preceding prime number: 421
Following prime number: 431