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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.
It gets harder as the numbers increase. You need to try dividing it by every Prime number up to the square root of the number in question. When you find a prime factor, divide the number by the factor and you will be left with a smaller number. Repeat until you reach the square root (if it is an integer). Whatever is left is the last factor. This gives you the prime factorisation.
Calculate the product for every subset of the prime factors. These will provide all the factors (except 1).
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What number has the biggest number of factors 60 or 100?
60 has more factors than 100 does.
What Numbers have 60 factors?
Any prime number to the 59th power will have 60 factors.
What composite number is between 45 and 60 and has factors of 2 and 25?
50
What is a special name for a number with the factors of 1234 and 5?
Any multiple of 60.
What is the different between factors and multiples?
The factors of a given number are those numbers which divide into the given number exactly without any remainder. The multiples of a given number are those numbers into which the given number divides exactly with no remainder (that is the given number's times table). example The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 since they all divide into 60 without any remainder The multiples of 60 are: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, (and so on) since they are all divisible by 60 with no remainder.
How do you find out the GCF of 45 60?
First you find the factors of 45 and 60. The Factors of 45 are:1,3,5,9,15,and 45 The Factors of 60 are:1,2,3,4,5,6,10,12,15,20,30,60 The GCF is the highest common number so the GCF is 15.
What is 17 over 60 simplified?
17 over 60 cannot be simplified because 17 is a prime number and has no factors in common with 60.
Find the smallest number that has 1 2 3 4 5 as factors?
That number is 60.
Find the smallest number having the following factors 3 4 5?
60
What number has the biggest number of factors 60 or 100?
60 has more factors than 100 does.
What Numbers have 60 factors?
Any prime number to the 59th power will have 60 factors.
What is the number between 60 and 70 that has an odd number of factors?
64 because 8*8=64. you just have to find the square number.
What is 77 over 60 as a mixed number?
77 over 60 as a mixed number = 117/60
What number has a factors of 23456?
Multiples of 60
What are the proper factors of the number 60?
2,3,4,5,6,10,12,15,20,30
What is the smallest number with twelve factors?
60
What is the lowest number with twelve factors?
60
