If you know the prime factorization of a number, you can find out the total number of factors.
Example: 210
21 x 31 x 51 x 71 = 210
Add one to the exponents and multiply them.
2 x 2 x 2 x 2 = 16, the total number of factors.
You know that 1, 2, 3, 5, and 7 are factors. You need three more to get halfway.
2 x 3 = 6
2 x 5 = 10
2 x 7 = 14
Divide all those numbers into 210.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
There is no universally easy (or hard) method. Some people might find one method easy and another difficult while others may well find the second easier and the first difficult.
The word "easier", in the question, implies that you know of at least one way but do not consider that to be particularly easy. But you have given no indication of what that way might be. I am therefore unable to work out what method you do know and offer an alternative.
Use some rules, then just guess.
All even numbers have 2 as a factor.
All numbers ending in 0 or 5 have 5 as a factor.
Add all the digits, if that is divisible by 3 or 9 then the original number will also have 3 or 9 as a factor.
If you know a list of squares, then (in your head) compare to the number you have.
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.
Try dividing it by small prime numbers.
- 2 is a factor of an even number.
- If the digits add to a multiple of 3, then the 3 is a factor.
- If the number ends in 0 or 5, then 5 is a factor.
- Try dividing by 7, 11, 13 etc. if none of these work.
by finding the half of the number and list the factors all the way to that number
Explaining how to find all factors pairs of 40 is easy. All you have to do is find which whole numbers 40 can be divided into.
All of them. Different numbers have different numbers of factors.
That depends what number you are trying to find the factors of - all those three numbers are factors of the number 18.
-- List all factors of the first number. -- List all factors of the second number. -- If there are more than two numbers, list all factors of each one. -- Find the set of factors that are on every list. -- Find the greatest factor in the set.
The prime factors of 51 are 3 and 17. Once you add itself and one, you have all the factors. (1,3,17,51)
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.
Explaining how to find all factors pairs of 40 is easy. All you have to do is find which whole numbers 40 can be divided into.
Factoring can be simple. In order to find the factors of a number, a person finds all the numbers that divide into the number evenly.
All factors of a number
The procedure to find all factors of a number are: 1) Separate the number into prime factors. 2) Try out all combinations of those factors.
Find out all the factors and then find the greatest common factor (gcf)...........very easy
All of them. Different numbers have different numbers of factors.
That depends what number you are trying to find the factors of - all those three numbers are factors of the number 18.
1,3,9 and27
To find out if a number is a square number, find its prime factors and check if all prime factors duplicate. In this example, the prime factors are: 2,2,5,5,5,5 We can see that all numbers are duplicates, and can be paired up. So 2500 is a square number of 2x5x5 or 50.
-- List all factors of the first number. -- List all factors of the second number. -- If there are more than two numbers, list all factors of each one. -- Find the set of factors that are on every list. -- Find the greatest factor in the set.
1,2,7,8,28,56