Using the prime factorization method find which of the following are perfect square 2592

Simplify Square Root of 2592

Inhaltsverzeichnis Show

How to Find the Factors of 2592?
What is the Sum of the Factors of 2592?
What are Prime Factors of 2592?
What is the Greatest Common Factor of 2592 and 545?
How Many Factors of 2592 are also Factors of 1458?

Here we will show you two methods that you can use to simplify the square root of 2592. In other words, we will show you how to find the square root of 2592 in its simplest radical form using two different methods. To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√2592 = A√B

Greatest Perfect Square Factor Method The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2592 to simplify the square root of 2592. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 2592. The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, and 2592. Furthermore, the greatest perfect square on this list is 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Calculate 2592 divided by the greatest perfect square from the list of all factors of 2592. We determined above that the greatest perfect square from the list of all factors of 2592 is 1296. Furthermore, 2592 divided by 1296 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 2592 in its simplest radical form as follows:

√2592 = A√B

√2592 = 36√2

Double Prime Factor Method The Double Prime Factor Method uses the prime factors of 2592 to simplify the square root of 2592 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 2592 and then take the square root of that product. The prime factors that multiply together to make 2592 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Divide 2592 by the number (A) squared. 36 squared is 1296 and 2592 divided by 1296 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 2592 in its simplest radical form as follows:

√2592 = A√B

√2592 = 36√2

Simplify Square Root Please enter another square root in the box below for us to simplify.

Simplify Square Root of 2593

Here is the next square root on our list that we have simplifed for you. Copyright | Privacy Policy | Disclaimer | Contact

Text Solution

Solution : By using prime factorization, `225=3times3times5times5=3times5`. Hence, `225` is a perfect square of `15`. By using prime factorization, `441=3times3times7times7=3times7`. Hence, `441` is a perfect square of `21`. By using prime factorization, `441=2times2times3times3times3times3times3times3=2times3times3times3`. Hence, `2916` is a perfect square of `54`. By using prime factorization, `11025=3times3times5times5times7times7=3times5times7`. Hence, `11025` is a perfect square of `105`.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.Morbi adipiscing gravdio, sit amet suscipit risus ultrices eu.Fusce viverra neque at purus laoreet consequa.Vivamus vulputate posuere nisl quis consequat.

Create an account

Find the smallest number by which 2592 be multiplied so that the product is a perfect square.

2592 = `bar(2xx2) xx bar(2xx2) xx 2 xx bar(3xx3) xx bar(3xx3)`

On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor.

2	2592
2	1296
2	648
2	324
2	162
3	81

The given number should be multiplied by 2 to make the given number a perfect square.

Concept: Finding Square Root Through Prime Factorisation

Is there an error in this question or solution?

Factors of 2592 are numbers that, when multiplied in pairs give the product as 2592. There are overall 30 factors of 2592 among which 2592 is the biggest factor and its prime factors are 2, 3. The Prime Factorization of 2592 is 25 × 34.

All Factors of 2592: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296 and 2592
Prime Factors of 2592: 2, 3
Prime Factorization of 2592: 25 × 34
Sum of Factors of 2592: 7623

Factors of 2592 are pairs of those numbers whose products result in 2592. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2592?

To find the factors of 2592, we will have to find the list of numbers that would divide 2592 without leaving any remainder.

2592/1 = 2592; therefore, 1 is a factor of 2592.
2592/12 = 216; therefore, 12 is a factor of 2592.

Similarly we can find other factors. Hence, the factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592.

☛ Also Check:

Factors of 57 - The factors of 57 are 1, 3, 19, 57
Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
Factors of 26 - The factors of 26 are 1, 2, 13, 26

The number 2592 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2592. The first step is to divide the number 2592 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

2592 ÷ 2 = 1296
1296 ÷ 2 = 648
648 ÷ 2 = 324
324 ÷ 2 = 162
162 ÷ 2 = 81

Further dividing 81 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 81 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 2592 can be written as 25 × 34 where 2, 3 are prime.

Pair factors of 2592 are the pairs of numbers that when multiplied give the product 2592. The factors of 2592 in pairs are:

1 × 2592 = (1, 2592)
2 × 1296 = (2, 1296)
3 × 864 = (3, 864)
4 × 648 = (4, 648)
6 × 432 = (6, 432)
8 × 324 = (8, 324)
9 × 288 = (9, 288)
12 × 216 = (12, 216)
16 × 162 = (16, 162)
18 × 144 = (18, 144)
24 × 108 = (24, 108)
27 × 96 = (27, 96)
32 × 81 = (32, 81)
36 × 72 = (36, 72)
48 × 54 = (48, 54)

Negative pair factors of 2592 are:

-1 × -2592 = (-1, -2592)
-2 × -1296 = (-2, -1296)
-3 × -864 = (-3, -864)
-4 × -648 = (-4, -648)
-6 × -432 = (-6, -432)
-8 × -324 = (-8, -324)
-9 × -288 = (-9, -288)
-12 × -216 = (-12, -216)
-16 × -162 = (-16, -162)
-18 × -144 = (-18, -144)
-24 × -108 = (-24, -108)
-27 × -96 = (-27, -96)
-32 × -81 = (-32, -81)
-36 × -72 = (-36, -72)
-48 × -54 = (-48, -54)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Example 1: How many factors are there for 2592?

Solution:

The factors of 2592 are too many, therefore if we can find the prime factorization of 2592, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 2592 = 25 × 34

Therefore, the total number of factors are (5 + 1) × (4 + 1) = 6 × 5 = 30

Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 2592 and 438.

Solution:

The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438.

Therefore, the Least Common Multiple (LCM) of 2592 and 438 is 189216 and Highest Common Factor (HCF) of 2592 and 438 is 6.

Example 3: Find if 9, 27, 32, 48, 144, 162, 288 and 1741 are factors of 2592.

Solution:

When we divide 2592 by 1741 it leaves a remainder. Therefore, the number 1741 is not a factor of 2592. All numbers except 1741 are factors of 2592.

Example 4: Find the product of all the prime factors of 2592.

Solution:

Since, the prime factors of 2592 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.

go to slidego to slidego to slidego to slide

Ready to see the world through math’s eyes?

Book a Free Trial Class

The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -81, -96, -108, -144, -162, -216, -288, -324, -432, -648, -864, -1296, -2592.

What is the Sum of the Factors of 2592?

Sum of all factors of 2592 = (25 + 1 - 1)/(2 - 1) × (34 + 1 - 1)/(3 - 1) = 7623

What are Prime Factors of 2592?

The prime factors of 2592 are 2, 3.

What is the Greatest Common Factor of 2592 and 545?

The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and the factors of 545 are 1, 5, 109, 545. 2592 and 545 have only one common factor which is 1. This implies that 2592 and 545 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2592 and 545 is 1.

How Many Factors of 2592 are also Factors of 1458?

Since, the factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and the factors of 1458 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458.
Hence, [1, 2, 3, 6, 9, 18, 27, 54, 81, 162] are the common factors of 2592 and 1458.