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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.
What else can I help you with?
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 the differences between a factor tree and a factor ladder?
Ah, the factor tree and the factor ladder are both wonderful ways to break down numbers into their factors. With a factor tree, you start with the number at the top and branch out into its prime factors. On the other hand, a factor ladder helps you list the factors in a more structured way, moving down in a step-by-step fashion. Both methods are like happy little tools in your math toolbox, ready to help you explore the beauty of numbers.
What is the factor tree for a composite number?
Oh honey, a factor tree is like a family tree for numbers. You start with the number on top and then branch out into its factors, breaking it down into smaller numbers until you can't break it down anymore. It's like a math version of "Who's Your Daddy?" for numbers.
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 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?!
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.
What is it called a way to breakdown a number into its factors?
factorizing
How long do rocks live and what factors contribute to their lifespan?
Rocks do not have a lifespan in the same way living organisms do. They can exist for millions or even billions of years, depending on factors like erosion, weathering, and geological processes. These factors can break down rocks over time, but they do not "die" in the traditional sense.
