How many factors are perfect cubes?

The factors of N = 216 are 2, 2, 2, 3, 3, 3. Therefore, number of factors that are perfect cube are (1 + 3/3) * (1 + 3/3) = 4. The factors are 1, 8, 27, and 216. Therefore, find the count of prime factors and apply the above formula to find the count of factors that are a perfect cube.

How do you calculate squares and cubes?

To square a number, multiply it by itself, e.g. \(\text{2} \times \text{2} = \text{2}^{\text{2}}= \text{4}\). To cube a number, multiply it by itself twice, e.g. \(\text{2} \times \text{2} \times \text{2} = \text{2}^{\text{3}} = \text{8}\).

Is 150 a cube number?

Is 150 a Perfect Cube? The number 150 on prime factorization gives 2 × 3 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 150 is irrational, hence 150 is not a perfect cube.

What is the formula for cube?

Cube and Cuboid Formulas

Cube	Cuboid
Volume of cube = (Side)3	Volume of the cuboid = (length × breadth × height)
Diagonal of a cube = √3l	Diagonal of the cuboid =√( l2 + b2 +h2)
Perimeter of cube = 12 x side	Perimeter of cuboid = 4 (length + breadth + height)

What are cubes and squares?

What are square and cube numbers? A square number is a number multiplied by itself. The square numbers up to 100 are: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. A cube number is a number multiplied by itself 3 times.

What is a perfect cube example?

A perfect cube is a number that is obtained by multiplying the same integer three times. For example, multiplying the number 4 three times results in 64. Therefore, perfect cube = number × number × number. The cube root of 64 is 4.

Are there any other formulas for factoring cubes?

The other two special factoring formulas you’ll need to memorize are very similar to one another; they’re the formulas for factoring the sums and the differences of cubes. Here are the two formulas: Factoring a Sum of Cubes: a 3 + b 3 = (a + b)(a 2 – ab + b 2)

How to factor perfect squares and perfect cubes?

Factoring (Perfect Squares and Cubes) Factoring Perfect Squares and Perfect Cubes Perfect Squares Perfect Cubes Back to Factoring The following is a list of perfect squares. 12= 1 22= 4 32= 9 42= 16 52= 25 62= 36 72= 49 82= 64 92= 81 102= 100 112= 121 122= 144 If a variable with an exponent has an even exponent then it is a perfect square.

How many cubes are in a number of squares?

Squares and Cubes table Squares (n2) Cubes (n3) Cubes (n3) Cubes (n3) 1 2 = 1 26 2 = 676 1 3 = 1 26 3 = 17576 2 2 = 4 27 2 = 729 2 3 = 8 27 3 = 19683 3 2 = 9 28 2 = 784 3 3 = 27 28 3 = 21952 4 2 = 16 29 2 = 841 4 3 = 64 29 3 = 24389

Which is the correct way to factor a difference of squares?

Actually, it’s both. You can factor this difference in either of two ways: factoring a difference of squares, followed by factoring the difference and sum of cubes: = ( x – 2) ( x + 2) ( x2 + 2 x + 4) ( x2 – 2 x + 4)