Is 245 a prime number?

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

For 245, the answer is: No, 245 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 245) is as follows: 1, 5, 7, 35, 49, 245.

For 245 to be a prime number, it would have been required that 245 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 245 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 245 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

245 is a multiple of 1
245 is a multiple of 5
245 is a multiple of 7
245 is a multiple of 35
245 is a multiple of 49

For 245 to be a prime number, it would have been required that 245 has only two divisors, i.e., itself and 1.

Is 245 a deficient number?

Yes, 245 is a deficient number, that is to say 245 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 245 without 245 itself (that is 1 + 5 + 7 + 35 + 49 = 97).

Parity of 245

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

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What is an even number?

Is 245 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 245 is about 15.652.

Thus, the square root of 245 is not an integer, and therefore 245 is not a square number.

What is the square number of 245?

The square of a number (here 245) is the result of the product of this number (245) by itself (i.e., 245 × 245); the square of 245 is sometimes called "raising 245 to the power 2", or "245 squared".

The square of 245 is 60 025 because 245 × 245 = 245² = 60 025.

As a consequence, 245 is the square root of 60 025.

Number of digits of 245

245 is a number with 3 digits.

What are the multiples of 245?

The multiples of 245 are all integers evenly divisible by 245, that is all numbers such that the remainder of the division by 245 is zero. There are infinitely many multiples of 245. The smallest multiples of 245 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 245 too, since 0 × 245 = 0
245: indeed, 245 is a multiple of itself, since 245 is evenly divisible by 245 (we have 245 / 245 = 1, so the remainder of this division is indeed zero)
490: indeed, 490 = 245 × 2
735: indeed, 735 = 245 × 3
980: indeed, 980 = 245 × 4
1 225: indeed, 1 225 = 245 × 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 245). 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 15.652). 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 245

Preceding numbers: …243, 244
Following numbers: 246, 247…

Nearest numbers from 245

Preceding prime number: 241
Following prime number: 251