Is 70 a prime number?

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

For 70, the answer is: No, 70 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 70) is as follows: 1, 2, 5, 7, 10, 14, 35, 70.

For 70 to be a prime number, it would have been required that 70 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 70 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 70 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

70 is a multiple of 1
70 is a multiple of 2
70 is a multiple of 5
70 is a multiple of 7
70 is a multiple of 10
70 is a multiple of 14
70 is a multiple of 35

For 70 to be a prime number, it would have been required that 70 has only two divisors, i.e., itself and 1.

Is 70 a deficient number?

No, 70 is not a deficient number: to be deficient, 70 should have been such that 70 is larger than the sum of its proper divisors, i.e., the divisors of 70 without 70 itself (that is 1 + 2 + 5 + 7 + 10 + 14 + 35 = 74).

In fact, 70 is an abundant number; 70 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 5 + 7 + 10 + 14 + 35 = 74). The smallest abundant number is 12.

Parity of 70

70 is an even number, because it is evenly divisible by 2: 70 / 2 = 35.

Find out more:

What is an even number?

Is 70 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 70 is about 8.367.

Thus, the square root of 70 is not an integer, and therefore 70 is not a square number.

What is the square number of 70?

The square of a number (here 70) is the result of the product of this number (70) by itself (i.e., 70 × 70); the square of 70 is sometimes called "raising 70 to the power 2", or "70 squared".

The square of 70 is 4 900 because 70 × 70 = 70² = 4 900.

As a consequence, 70 is the square root of 4 900.

Number of digits of 70

70 is a number with 2 digits.

What are the multiples of 70?

The multiples of 70 are all integers evenly divisible by 70, that is all numbers such that the remainder of the division by 70 is zero. There are infinitely many multiples of 70. The smallest multiples of 70 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 70 too, since 0 × 70 = 0
70: indeed, 70 is a multiple of itself, since 70 is evenly divisible by 70 (we have 70 / 70 = 1, so the remainder of this division is indeed zero)
140: indeed, 140 = 70 × 2
210: indeed, 210 = 70 × 3
280: indeed, 280 = 70 × 4
350: indeed, 350 = 70 × 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 70). 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 8.367). 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 70

Preceding numbers: …68, 69
Following numbers: 71, 72…

Nearest numbers from 70

Preceding prime number: 67
Following prime number: 71