Is 49 a prime number? What are the divisors of 49?

Is 49 a prime number?

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

For 49, the answer is: No, 49 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 49) is as follows: 1, 7, 49.

To be 49 a prime number, it would have been required that 49 has only two divisors, i.e., itself and 1.

As a consequence:

  • 49 is a multiple of 1
  • 49 is a multiple of 7

To be 49 a prime number, it would have been required that 49 has only two divisors, i.e., itself and 1.

However, 49 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 49 = 7 x 7, where 7 is a prime number.

Is 49 a deficient number?

Yes, 49 is a deficient number, that is to say 49 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 49 without 49 itself (that is 1 + 7 = 8).

Parity of 49

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

Is 49 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 49 is 7.

Therefore, the square root of 49 is an integer, and as a consequence 49 is a perfect square.

As a consequence, 7 is the square root of 49.

What is the square number of 49?

The square of a number (here 49) is the result of the product of this number (49) by itself (i.e., 49 × 49); the square of 49 is sometimes called "raising 49 to the power 2", or "49 squared".

The square of 49 is 2 401 because 49 × 49 = 492 = 2 401.

As a consequence, 49 is the square root of 2 401.

Number of digits of 49

49 is a number with 2 digits.

What are the multiples of 49?

The multiples of 49 are all integers evenly divisible by 49, that is all numbers such that the remainder of the division by 49 is zero. There are infinitely many multiples of 49. The smallest multiples of 49 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 49 too, since 0 × 49 = 0
  • 49: indeed, 49 is a multiple of itself, since 49 is evenly divisible by 49 (we have 49 / 49 = 1, so the remainder of this division is indeed zero)
  • 98: indeed, 98 = 49 × 2
  • 147: indeed, 147 = 49 × 3
  • 196: indeed, 196 = 49 × 4
  • 245: indeed, 245 = 49 × 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 49). 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 7). 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 49

  • Preceding numbers: …47, 48
  • Following numbers: 50, 51

Nearest numbers from 49

  • Preceding prime number: 47
  • Following prime number: 53
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