Squarefree Integer Calculator

Welcome to the Squarefree Integer Calculator, which can quickly help you check if a number is a squarefree integer.

Squarefree Integer Calculator

Eg, Is 25 a squarefree integer? Enter 25 into the input box and click Calculate button.

What is a squarefree integer?

Like its name, a squarefree integer (or square-free integer) is an integer whose factors are not square except 1. In other words, after prime factorization of a positive integer, none of the prime factors are repeated, then this positive integer is called a squarefree integer.

For example, Is 12 a squarefree integer?

The factors of 12 are 1, 2, 4, 6 and 12. Among them, 4 is a perfect square number. So, 12 is not a squarefree integer. Another way, through the prime factorization calculator, we can get that the prime factorization of 12 is

12 = 2 * 2 * 3

Obviously, 2 is repeated. Therefore, 12 is not a squarefree integer.

Another example, Is 30 a squarefree integer?

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. None of these factors are perfect squares. The second method, the prime factorization of 30 is

30 = 2 * 3 * 5

No repeating prime factors. So, 30 is a squarefree integer.

First 100 squarefree integers

1	2	3	5	6	7	10	11	13	14
15	17	19	21	22	23	26	29	30	31
33	34	35	37	38	39	41	42	43	46
47	51	53	55	57	58	59	61	62	65
66	67	69	70	71	73	74	77	78	79
82	83	85	86	87	89	91	93	94	95
97	101	102	103	105	106	107	109	110	111
113	114	115	118	119	122	123	127	129	130
131	133	134	137	138	139	141	142	143	145
146	149	151	154	155	157	158	159	161	163

How to use the squarefree integer calculator

The procedure to use the squarefree integer calculator is as follows:

1Enter the positive number.
2Click Calculate button to verify whether the input number is a squarefree integer.
3Click the Reset button to start a new verification.

Solved examples using the squarefree integer calculator

Example 1: Is 25 a squarefree integer?

Enter 25 into the input box and click Calculate button, as shown in the figure, 25 is not a squarefree integer.

The prime factorization of 25 is

25 = 5 * 5 = 5²

Obviously, 5 is repeated. So, 25 is not a squarefree integer.

Example 2: Is 430 a squarefree integer?

Enter 430 into the input box and click Calculate button, as shown in the figure, 430 is a squarefree integer.

The prime factorization of 430 is

25 = 2 * 5 * 43

No prime factors are repeated. So, 430 is a squarefree integer.

Squarefree Integer Calculator