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There are a few ways to go about factoring. You can decide what works best for you. I always find the prime factorization first. Let's look at a random number: 108
The prime factorization can be found by using a factor tree.
108
54,2
27,2,2
9,3,2,2
3,3,3,2,2
2^2 x 3^3 = 108
Half of the factors will be less than the square root, half greater. If the number is a perfect square, there will be an equal number of factors on either side of the square root. In this case, the square root is between 10 and 11.
Adding one to the exponents of the prime factorization and multiplying them will tell you how many factors there are. In this case, the exponents are 2 and 3. Add one to each. 3 x 4 = 12
108 has 12 factors. Six of them are 10 or less, six of them are 11 or greater. All we have to do is divide the numbers one through ten into 108. If the result (quotient) turns out to be an integer, you've found a factor pair. Knowing the rules of divisibility will make that even easier.
108 is divisible by...
1 because everything is.
2 because it's even.
3 because its digits add up to a multiple of 3.
4 because its last two digits are a multiple of 4.
6 because it's a multiple of 2 and 3.
9 because its digits add up to a multiple of 9.
That's six factors less than 10. Divide them into 108. That's the rest of them.
(108,1)(54,2)(36,3)(27,4)(18,6)(12,9)
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Notice that all of those numbers, except for 1, can also be found in the prime factorization.
The simplest way is to try out different factors. Try if the number is divisible by 2, 3, 5, 7 (trying out those factors is enough for numbers up to 120); if you find one, divide by that factor, and separate the rest of the number. For example, since 88 is a multiple of 2, you divide it by 2 to get 44, so you write:
88 = 2 x 44
Then continue looking whether there are additional factors for 44, in this case (or whatever is left, for other numbers).
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Does it matter what two factors you select to a factor tree explain?
No. Since you are going to keep factoring until all the factors are prime, it doesn't matter what you start with. Example: 36 You can start with 6 and 6, which you would then break down into 2,3,2,3. You could start with 9 and 4, which you would then break down to 3,3,2,2. Either way, you're going to wind up with two twos and two threes. 2 x 2 x 3 x 3 is the prime factorization for 36.
How do you do factor trees?
You break down the factors of a number until all the factors are prime. For example: 24 / \ 6 4 / \ 3x2 x 2x2 This factor tree was very easy, but there will be harder ones in the future. When all the numbers at the bottom of the tree are prime, you are finished. Factor trees may also be used to find the prime factorization of a number. PS: I'm sorry about the appearance of the tree. Once I published it, it became, and stayed that way. Real factor trees don't look like this. 24 is broken down into 6x4, because they are the factors. Since 24 is composite, you do not have to use 6x4. Then we break 6 into 3x2, and 4 into 2x2. Then 3x2x2x2 is a prime factorization. And you are also done with the factor tree!
Which number between 21 and 40 has the most factors?
The number with the most factors between 21 and 40 is 30. Factors of a number are the numbers that can divide the original number without leaving a remainder. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, giving it a total of 8 factors, which is the highest among the numbers between 21 and 40.
What is 49 divisible by?
A number being divisible by another number is a different way of saying the factors of a number. Factors are numbers you can multiply together to get another number. 49: 1, 7, 49
What is the difference between foil and factor?
FOIL is a way to combine terms through multiplication. Factoring is a way to break down terms through division.
How can you break down numbers?
The best way to break down a number (from the perspective of arithmetic!) is to write it as a product of its prime factors. For instance, 24 = 2 x 3 x 4 where x is the multiplication operator and of course 2, 3, and 4 are all prime numbers.
What does break the second number down into factors to work out 18x18?
Ok I'll guess 18x18 = 18x9x2 = (18x9)x2 = 162x2 = 324 or = 18x6x3 = (18x6)x3 = 108x3 = 324 same answer either way
What are the equation to show a way to break down each number 24 and 18?
20+4=24
The only way to break down a compound is through a?
The only way to break down a compound is through a chemical reaction.
Does it matter what two factors you select to a factor tree explain?
No. Since you are going to keep factoring until all the factors are prime, it doesn't matter what you start with. Example: 36 You can start with 6 and 6, which you would then break down into 2,3,2,3. You could start with 9 and 4, which you would then break down to 3,3,2,2. Either way, you're going to wind up with two twos and two threes. 2 x 2 x 3 x 3 is the prime factorization for 36.
How do you break down the word vegetables into syllables?
Vege-ta-bles. An easy way to count syllables is to count the number of times your jaw goes down while you are saying a word.
What is the quickest way to break down alcohol levels in your blood?
There isn't a "quick way" to break down alcohol levels in your body. Showering, coffee, water, etc.. all a myth.
How much years does a water bottle need to break down?
It typically takes a plastic water bottle between 450 and 1,000 years to break down in the environment. Factors such as exposure to sunlight, heat, and mechanical stress can speed up or slow down the degradation process. Recycling is the best way to minimize the environmental impact of plastic bottles.
How do mammals break down food?
the same way yours breaks down~ WITH THERE STOMACH ACID
How do you get your rear windows to go All the way down in your 2012 maxima?
They don't go all the way down. You could break them?!
What is it called a way to breakdown a number into its factors?
factorizing
List all the factors of 62?
To find the factors of a number, I suggest using a factor tree. It is elementary, but it is undeniably the simplest way. Start with the number, in this case 62.62Pick any two factors and write them under the original number.622 x 31Circle (or bold) the prime numbers. These can no longer be divided. (In this case, both factors of 62 are prime. Otherwise, you would further break down the actors until you are only left with primes)In conclusion, the factors of 62 are 1, 2, 31, and 62. 2 and 31 are the prime factors of 62.
