Is 126 a prime number? What are the divisors of 126?

Is 126 a prime number?

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

For 126, the answer is: No, 126 is not a prime number.

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

To be 126 a prime number, it would have been required that 126 has only two divisors, i.e., itself and 1.

As a consequence:

  • 126 is a multiple of 1
  • 126 is a multiple of 2
  • 126 is a multiple of 3
  • 126 is a multiple of 6
  • 126 is a multiple of 7
  • 126 is a multiple of 9
  • 126 is a multiple of 14
  • 126 is a multiple of 18
  • 126 is a multiple of 21
  • 126 is a multiple of 42
  • 126 is a multiple of 63

To be 126 a prime number, it would have been required that 126 has only two divisors, i.e., itself and 1.

Is 126 a deficient number?

No, 126 is not a deficient number: to be deficient, 126 should have been such that 126 is larger than the sum of its proper divisors, i.e., the divisors of 126 without 126 itself (that is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 = 186).

In fact, 126 is an abundant number; 126 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 = 186). The smallest abundant number is 12.

Parity of 126

126 is an even number, because it is evenly divisible by 2: 126 / 2 = 63.

Is 126 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 126 is about 11.225.

Thus, the square root of 126 is not an integer, and therefore 126 is not a square number.

What is the square number of 126?

The square of a number (here 126) is the result of the product of this number (126) by itself (i.e., 126 × 126); the square of 126 is sometimes called "raising 126 to the power 2", or "126 squared".

The square of 126 is 15 876 because 126 × 126 = 1262 = 15 876.

As a consequence, 126 is the square root of 15 876.

Number of digits of 126

126 is a number with 3 digits.

What are the multiples of 126?

The multiples of 126 are all integers evenly divisible by 126, that is all numbers such that the remainder of the division by 126 is zero. There are infinitely many multiples of 126. The smallest multiples of 126 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 126 too, since 0 × 126 = 0
  • 126: indeed, 126 is a multiple of itself, since 126 is evenly divisible by 126 (we have 126 / 126 = 1, so the remainder of this division is indeed zero)
  • 252: indeed, 252 = 126 × 2
  • 378: indeed, 378 = 126 × 3
  • 504: indeed, 504 = 126 × 4
  • 630: indeed, 630 = 126 × 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 126). 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 11.225). 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 126

  • Preceding numbers: …124, 125
  • Following numbers: 127, 128

Nearest numbers from 126

  • Preceding prime number: 113
  • Following prime number: 127
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