Is 672 a prime number?

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

For 672, the answer is: No, 672 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 672) is as follows: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.

For 672 to be a prime number, it would have been required that 672 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

672 is a multiple of 1
672 is a multiple of 2
672 is a multiple of 3
672 is a multiple of 4
672 is a multiple of 6
672 is a multiple of 7
672 is a multiple of 8
672 is a multiple of 12
672 is a multiple of 14
672 is a multiple of 16
672 is a multiple of 21
672 is a multiple of 24
672 is a multiple of 28
672 is a multiple of 32
672 is a multiple of 42
672 is a multiple of 48
672 is a multiple of 56
672 is a multiple of 84
672 is a multiple of 96
672 is a multiple of 112
672 is a multiple of 168
672 is a multiple of 224
672 is a multiple of 336

For 672 to be a prime number, it would have been required that 672 has only two divisors, i.e., itself and 1.

Is 672 a deficient number?

No, 672 is not a deficient number: to be deficient, 672 should have been such that 672 is larger than the sum of its proper divisors, i.e., the divisors of 672 without 672 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 32 + 42 + 48 + 56 + 84 + 96 + 112 + 168 + 224 + 336 = 1 344).

In fact, 672 is an abundant number; 672 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 32 + 42 + 48 + 56 + 84 + 96 + 112 + 168 + 224 + 336 = 1 344). The smallest abundant number is 12.

Parity of 672

672 is an even number, because it is evenly divisible by 2: 672 / 2 = 336.

Find out more:

What is an even number?

Is 672 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 672 is about 25.923.

Thus, the square root of 672 is not an integer, and therefore 672 is not a square number.

What is the square number of 672?

The square of a number (here 672) is the result of the product of this number (672) by itself (i.e., 672 × 672); the square of 672 is sometimes called "raising 672 to the power 2", or "672 squared".

The square of 672 is 451 584 because 672 × 672 = 672² = 451 584.

As a consequence, 672 is the square root of 451 584.

Number of digits of 672

672 is a number with 3 digits.

What are the multiples of 672?

The multiples of 672 are all integers evenly divisible by 672, that is all numbers such that the remainder of the division by 672 is zero. There are infinitely many multiples of 672. The smallest multiples of 672 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 672 too, since 0 × 672 = 0
672: indeed, 672 is a multiple of itself, since 672 is evenly divisible by 672 (we have 672 / 672 = 1, so the remainder of this division is indeed zero)
1 344: indeed, 1 344 = 672 × 2
2 016: indeed, 2 016 = 672 × 3
2 688: indeed, 2 688 = 672 × 4
3 360: indeed, 3 360 = 672 × 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 672). 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 25.923). 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 672

Preceding numbers: …670, 671
Following numbers: 673, 674…

Nearest numbers from 672

Preceding prime number: 661
Following prime number: 673