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# How do you know when you've found all the factors for a number?

Updated: 8/30/2023

Wiki User

11y ago

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

You know you've found all the factors of a number when the next first factor exceeds its corresponding second factor. For example, after you found that 4 was a factor of 24 and 5 was not, you would see that 6, the next factor of 24, had already been included in a pair of factors. Thus, all the factors have been found.

Wiki User

11y ago

Wiki User

9y ago

There is no simple way to find the answer to the question in general. The question needs to be more specific.

Wiki User

12y ago

Every number is both a factor and a multiple of itself. Every other factor is smaller than the number, every other multiple is larger than the number.

Wiki User

9y ago

Use multiples when you're adding or subtracting them.

Use factors when you're reducing them.

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All of the factors are prime.

### How do you know when you have found the longest factor string for a number?

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### Do numbers always have more than two factors?

No, an odd number can have any number of factors. There is no limit but you do know that the number 2 is not one of those factors.

### What do we know about a number that has an odd number of distinct factors?

It's a perfect square.

Divisibility rules help you find the factors of a number. Once you've found the factors for two or more numbers, you can find what they have in common. Take 231 and 321. If you know the divisibility rules, you know that they are both divisible by 3, so 3 is a common factor.

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How to know that you found all the factors for example my teacher taught me that when u reach a double diget number that is all the factors. ( 6x6)-~ double diget number

### How do you know when you've found all the factors of a number?

If you multiply all the prime factors you've found together and the result is the number, you have found all of them.

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When all the factors are prime.

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### How do you know if a number is abundant or deficiant?

First to be able to find an abundant number you have find all the factors of any number. Then add them all up. If the total is bigger than the number you found out the factors of then it is an abundant number and if the total is less than the number you found out the factors for it is a deficiant number and finally if the total is the same number as the one you found out the factors for it is called a perfect number. Thanks for learning from me. I hope you have understood what i have typed. Bye!

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