Powerful Number Checker

Powerful Number Checker is a free online tool used to check if the given number is a powerful number.

Powerful Number Checker

Eg, Is 2025 a powerful number? Enter 2025 into the input box and click Calculate button.

What is a powerful number?

A positive integer m is called as a powerful number, when for every prime number p that divides m, and p² also divides m. It can also be explained as a number that is the product of a square and a cube. So, a number m, which can be stated as the form m = a²b³ for positive integers a and b is a powerful number. The other names of Powerful numbers are squareful, square-full, or 2-full.

For example, 64 is a powerful number.

With find all factors calculator, we can get that the factors of 64 are 1, 2, 4, 8, 16, 32 and 64. Among them, 2 is a prime factor. 2² = 4 is also a factor of 64. So, 64 is a powerful number.

First 100 powerful numbers

625
648
675
676
729
784
800
841
864
900
961
968
972
1000
1024
1089
1125
1152
1156
1225

1296
1323
1331
1352
1369
1372
1444
1521
1568
1600
1681
1728
1764
1800
1849
1936
1944
2000
2025
2048

2116
2187
2197
2209
2304
2312
2401
2500
2592
2601
2700
2704
2744
2809
2888
2916
3025
3087
3125
3136

How to use the powerful number checker

The procedure to use the powerful number checker is as follows:

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

Solved examples using the powerful number checker

Example 1: Is 1024 a powerful number?

Enter 1024 into the input box and click Calculate button, as shown in the figure, 1024 is a powerful number.

Example 2: Is 3888 a powerful number?

Enter 3888 into the input box and click Calculate button, as shown in the figure, 3888 is a powerful number.

Powerful Number Checker