Prime Factorization Method to Find the Cube of 5832

To find the cube of 5832 using the prime factorization method, we need to break down the number into its prime factors and then multiply them together three times.

Step 1: Prime Factorization of 5832

To find the prime factorization of 5832, we divide the number by prime numbers starting from 2 until we cannot divide any further.

5832 ÷ 2 = 2916
2916 ÷ 2 = 1458
1458 ÷ 2 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 5832 is 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3.

Step 2: Write the Prime Factors in Triplets

To find the cube of 5832, we group the prime factors in triplets because we are finding the cube.

2 × 2 × 2 = 8
3 × 3 × 3 = 27

Therefore, 5832 can be written as (2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3).

Step 3: Simplify the Expression

Now, we simplify the expression by multiplying the prime factors together.

(2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3) = 8 × 27 × 27

Step 4: Calculate the Cube

Finally, we calculate the cube by multiplying the simplified expression together.

8 × 27 × 27 = 5832

Therefore, the cube of 5832 is 5832.

Conclusion

Using the prime factorization method, we can find the cube of a number by breaking it down into its prime factors and then multiplying them together three times. In this case, the cube of 5832 is 5832.

5832= 2×2×2×3×3×3×3×3×3=2^3×3^3×3^3= 18^3
So, cube root of 5832 is 18