If its an even number it will divide by '2'
If it end in '0' or '5' it will dividfe by '5'.
If neither of them work, then try '3' followed by '7'.
Fiunally if the duguts of a number sum to '9' , then it will divide , '9'.
e.g. Factors of 24.
It ends in an even number '4'
So
2)24 = 12
Keep on dividing by '2'
2)12 = 6
2)6 = 3
Since it is now an odd number , use '3'.
So all the factors of 24 are 2,2,2,& 3.
Try say , 15
Since it ends in '5' it will divide by '5'
Hence 5)15 = 3
No further division by '5' , then use '3'
Hence the factors of 15 are 3,5.
Hence try '81'
8 + 1 = 9
So 9)81 = 9
9'9' is factor of '3'
Hence 3) 9 = 3
3)3 = 1
Since there two x '9' we must do this asecond time.
Hence 3)9 = 3
3)3 = 1
Hence the factortsd of 81 ar 3,3,3,&3.
NB When testing for factors, always use prime numbers. 2,3,5,7,11,13,,17 ,19 etc.,
Chat with our AI personalities
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.
You figure out a number's factors by figuring out what can be multiplied by any number to equal that number, like the factors of 10 are 1, 2, 5, and 10. :D
180: it has 18 factors.
It wasn't me, but I would have come up with 33. The four factors of 33 add up to 48.
Pairs of numbers whose sum is -14 and that are factors of -189 include -7 and -7, and -21 and 7.
All nonzero numbers have factors. Some numbers have some of the same factors as other numbers. These are called common factors. Some factors are positive numbers. Common factors which are positive numbers would be called positive common factors.
All numbers have factors. The factors that are positive numbers are known as positive factors.