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Using the division method to find prime factors
- let x be the number to be factorised
- let p be the lowest Prime number below the square root of x (always 2, unless x is below 4)
- Calculate x/p
- if x/p was an integer, update the list of factors to include p and let x = x/p
- if x > 1 and p < √x, return to step 3
- you now have your completed list
So, to find the prime factors of 75600, just follow the instructions.
75600/2 = 37800[2] 37800/2 = 18900[2] 18900/2 = 9450[2] 9450/2 = 4725[2] 4725/2 = 2362.5 4725/3 = 1575[3] 1575/3 = 525[3] 525/3 = 175[3] 175/3 = 58.3 175/5 = 35[5] 35/5 = 7[5] 7[7]
So, 75600 = 2x2x2x2x3x3x3x5x5x7 = 24x33x52x7
A full list of factors could be arranged from this, by multiplying different prime factors together.
Ie.
75600, 37800, 25200, 18900, 15120, 12600, 10800, 9450, 8400, 7560, 6300, 5400, 5040, 4725, 4200, 3780, 3600, 3150, 3024, 2800, 2700, 2520, 2160, 2100, 1890, 1800, 1680, 1575, 1512, 1400, 1350, 1260, 1200, 1080, 1050, 1008, 945, 900, 840, 756, 720, 700, 675, 630, 600, 560, 540, 525, 504, 450, 432, 420, 400, 378, 360, 350, 336, 315, 300, 280, 270, 252, 240, 225, 216, 210, 200, 189, 180, 175, 168, 150, 144, 140, 135, 126, 120, 112, 108, 105, 100, 90, 84, 80, 75, 72, 70, 63, 60, 56, 54, 50, 48, 45, 42, 40, 36, 35, 30, 28, 27, 25, 24, 21, 20, 18, 16, 15, 14, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
To find the number of different factors of a number, factorize the number into its prime factors. For 75600, the prime factorization is 2^4 * 3^3 * 5^2 * 7. Now, add 1 to the exponent of each prime factor and multiply the results: (4+1) * (3+1) * (2+1) * (1+1) = 5 * 4 * 3 * 2 = 120. Therefore, the number 75600 has 120 different factors.
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How do you find out if a number is a prime or composite number?
Find the factors of the number. If the only factors are 1 and itself, it is prime.A prime number is a positive integer with two factors: one and the number itself.A composite number is a positive integer with more than two factors.
How do you find the prime factors of a squared number?
The prime factors of a squared number are the prime factors, if any, of its square root.
What are the factors for number 65?
To find the factors of a number you should first break that number down into its prime factors. In this case 65 can be broken down as: 65 = 5x13 To find any other factors, you then multiply any combination of these prime factors together. In this case, the factors of 65 come out as: 1, 5, 13 and 65.
What number has 13 number factors?
"Factors come in pairs, so this is impossible." This statement is false. A number can have an odd number of factors by having the square root as one of the factors. Find a number with 12 factors and a square root.
Is 799 a prime number?
No, but it is hard to find factors.
How many factors do you have to list when it asks you find all of the whole number factors?
All of them. Different numbers have different numbers of factors.
How is prime factorization different from finding factors of a number?
All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.
Is it possible to find different ways to multiply the same number of factors of 120 180 210?
Yes.
How do you find out if a number is a prime or composite number?
Find the factors of the number. If the only factors are 1 and itself, it is prime.A prime number is a positive integer with two factors: one and the number itself.A composite number is a positive integer with more than two factors.
How is factoring a polynomial different from multiplying two binomials?
The same way that factoring a number is different from multiplying two factors. In general, it is much easier to multiply two factors together, than to find factors that give a certain product.
Would you rather find all the factors of a number or find all the prime factors of a number?
Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.
Help you find out the factors of a prime number?
Any prime number has two factors: 1 and the number itself.
How do you find the prime factors of a squared number?
The prime factors of a squared number are the prime factors, if any, of its square root.
Can negative numbers have factors?
Sure. Take any positive number and find its factors. Then, if you make an odd number of the factors negative, you then have a set of factors of the negative of the original composite number. That means that the factors of a negative number are not 'unique'. Take ' 6 ' for example. Its factors are 1, 2, 3, and 6. If you make the '1' or the '2' or the '3' or the '6' negative, then you have four factors of ' -6 '. Are there any other ways to make an odd number of them negative ? I see eight different ways to make an odd number of those four numbers negative. So ' -6 ' has eight different possible sets of factors. Is that weird or what !
How do you find a mixed number?
you find a mixed number by dividing a number by one of the alike factors and then you have it
How many factors any number has limited or unlimited?
every number has a limited amount of factors those you could chose any number and find another with that number of factors
Can I find the greatest number with factors 112337?
No.
