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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.
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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.
What are the common factors of 245?
Factors are numbers we can multiply together to get another number: Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A number can have MANY factors!So, an easy way of finding your answers is to look at a timetable charts and analyze what equals to 2,4 and #5.
What is the factor rainbow for 9?
List the number at the bottom. Break it down into factors by placing them on successive lines above the original number. Stop when all the factors are prime. 7,5,3,2 35,3,2 105,2 210
What are the common factor of 21 and 27?
A factor is a divisor - a number that will evenly divide into another number. One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them. The factors of 21 are 1, 3, 7, and 21. The factors of 27 are 1, 3, 9, and 27. The common factors are 1 and 3. This means that the greatest common factor is 3.
What is the only way to create a factor tree?
Write the composite number you want to factor on a piece of paper. Write one of its factor pairs underneath it. If possible, keep breaking each factor down until all the factors are prime. All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime.
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.
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.
Which two pairs of numbers have 10 as their least common multiple?
The way to work this out is to break the number down into its prime factors. In this case, 10 can be expressed as 2x5. Thus two numbers will have 10 as a common multiple if the only unique factors between them is a single 2 and a single 5. This can be achieved with the following pairs: 1 and 10 2 and 10 5 and 10 2 and 5
