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Factor of 256

256 is a composite number having all the factors which can be observed in table of 2, 4 and 8. Hence each pair factor of 256 includes atleast one number which is divisible by 2. Let us explore more about factors of 256 with some interesting examples.

Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128 and 256.
Prime Factorization of 256: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

1.	What Are the Factors of 256?
2.	How to Calculate Factors of 256?
3.	Factors of 256 by Prime Factorization
4.	Factors of 256 in Pairs
5.	FAQs-on-Factors-of-256

What are the Factors of 256?

Factors of 256 are all the numbers that on multiplication give the product 256.

factors of 256

How to Calculate the Factors of 256?

The factors of 256 are integers that divide 256 without any remainder.

Let's learn how to calculate factors of 256.
Let's begin calculating the factors of 256, starting with1.
256 ÷ 1 = 256, Remainder = 0
256 ÷ 2 = 128, Remainder = 0
256 ÷ 4 = 64, Remainder = 0
256 ÷ 8 = 34, Remainder = 0
256 ÷ 16 = 16 Remainder = 0
All the divisors and the quotient thus obtained on division form the factors of 256. They are: 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Hence, the factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Explore factors using illustrations and interactive examples.

Factors of 250: The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
Factors of 625: The factors of 625 are 1, 5, 25, 125 and 625.
Factors of 32: The factors of 32 are 1, 2, 4, 8, 16, and 32.
Factors of 216: The factors of 216 are , 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216
Factors of 25: The factors of 25 are 1, 5 and 25

Factors of 256 by Prime Factorization

Prime factorization is to express a composite number as the product of its prime factors.

To get the prime factorization of 256, we divide it by its smallest prime factor which is 5. 256 ÷ 2 = 128,
Now divide 128 by its smallest prime factor. 128 ÷ 2 =64
This process goes on till we get the quotient as 1.
The prime factorization of 256 is shown below in 2 ways: factor-tree method and the upside-down division method.

prime factorization of 256

256 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2. We can multiply all of these factors thus obtained and get all the possible composite factors as well.

Factors of 256 in Pairs

The pair of numbers that multiply together to form 256 are said to be the factors of 256 in pairs. The distinct factor-pairs of 256 is given as (1, 256), (2, 128), (4, 64), (8, 32), and (16, 16). We can have positive and negative factors that make 256. The negative factor-pairs of 256 are (-1, -256), (-2, -128), (-4, -64), (-8, -32), and (-16, -16).

Important Notes

As 256 is an even number, all of its factors will also be even.
256 is a perfect square number.
Factors are never fractions or decimals.

Example 1: Jane plays a game using two dice.She makes a two-digit number that turns up on the faces of both the dice. For each two-digit number, find out if in any of three rounds she got a common factor of 256 and 144

Rounds Factor pairs

Round 1 6, 3

Round 2 1, 6

Round 3 4, 6

Solution:

Let's see the factors of 256 and 144
- Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128 and 256
- Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
Now, let's see the numbers formed by Jolly in both rounds.
- In round 1, Jane got the pair 6 and 3. The 2-digit numbers that can be formed are 36 and 63.
36 is a factor of 144. However, 63 is neither a factor of 256 nor a factor of 144.
- In round 2, Jane got the pair 1 and 6. The 2-digit numbers that can be formed are16 and 61.
16 is a factor of 256 and also a factor of 144. On the other hand, 61 is neither a factor of 256 nor 144
- In round 3, Jane got the pair 4 and 6. The 2-digit numbers that can be formed are 46 and 64.
64 is a factor of 256. On the other hand, 46 is neither a factor of 256 nor 144.
Therefore she got 16 in the 2nd round which is a common factor of 256 and 144.
Example 2: Sam bought 256 apples, 128 oranges, and 64 avocados from the fruit shop. Sam plans to visit an orphanage to provide fruits.Help Sam to prepare 64 fruit bags in such a way that each bag should have the same number and type of fruit.

Solution:

There are 256 apples, 128 oranges, and 64 avocados.

Sam must prepare 64 fruit bags.
- 256 ÷ 64= 4
- 128 ÷ 64= 2
- 64 ÷ 64= 1
Therefore each bag should have 4 apples, 2 oranges, and 1 avocado.

Rounds	Factor pairs
Round 1	6, 3
Round 2	1, 6
Round 3	4, 6

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FAQs on Factors of 256

How many of the factors of 256 are perfect squares?

There are 5 factors of 256 which are perfect squares. 1, 4, 16, 64, and 256 are all perfect squares.

Is 256 a perfect square?

256 is a perfect square, as it is expressed as 16 x 16.

What are the factors of 256?

1, 2, 4, 8, 16, 32, 64, 128 and 256.

What are the factors of 256 and 255?

1, 2, 4, 8, 16, 32, 64, 128 and 256.

The factors of 255 are 1, 3, 5, 15, 17, 51, 85, and 255

Is 256 a perfect cube?

256 cannot be expressed as number × number × number(the product of triples). Therefore it is not a perfect cube.

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