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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
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Why do you need to know all of the factors to a number to know if it is a prime or composite number?
You don't.If you know just one factor, other than 1 and the number itself, you will know that the number is composite.A prime has only two factors: 1 and itself. So all the factors is no big deal.
Do you need to know all of the factors of a number to know it is prime or composite?
To know that a number is prime you need to know that it has no factors other than 1 and the number itself.To know that a number is composite you only need to know one factor other than the number itself or 1.
How do you know when you have found all the prime factors?
If all the factors are prime numbers and they total the original number, you have found them all. All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.
How do you know when you have found all the possible factors for a number?
Let's suppose you've already listed out all the factors you can find for a number, and want to know if that's all of them. To find this, find the prime factorization of the number (should be quite easy when you know all the factors). e.g. 540 = 2^2 * 3^3 * 5. Now you can find the number of factors by a simple formula: since the exponent on 2 is 2, the exponent on 3 is 3, and the exponent on 5 is 1, you calculate (2+1)*(3+1)*(1+1)=3*4*2=24. There are 24 factors, including 1 and 540. So count all the factors you have, and if you have 24, you've found all of them. To remember that formula, notice that all factors of 540 are of the form 2^x*3^y*5^z with 0≤x≤2, 0≤y≤3, and 0≤z≤1. There are 3 different possible exponents for 2, 4 for 3, and 2 for 5, so the number of ways they can combine is 3*4*2.
How do you know when you have found the longest possible factor string of a number?
When all of the numbers are prime.
How do you know you found all factors to a number?
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.
How do you know when you have found the longest string of factors for a number?
When all the factors are prime.
How do you know when you have found the longest possible sting factors of a number?
All of the factors are prime.
How do you know when you have found the longest factor string for a number?
All of the factors are prime.
When looking for a factors of a composite number how do you know you have found the right answer?
List them all, and multiply to see if you get the original number.
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!
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.
Why do you need to know all of the factors to a number to know if it is a prime or composite number?
You don't.If you know just one factor, other than 1 and the number itself, you will know that the number is composite.A prime has only two factors: 1 and itself. So all the factors is no big deal.
Do you need to know all of the factors of a number to know it is prime or composite?
To know that a number is prime you need to know that it has no factors other than 1 and the number itself.To know that a number is composite you only need to know one factor other than the number itself or 1.
Do you need to know all of the factors of a number in order to determine if it is prime or composite?
No because, all you have to know is your multiplication to help you.
How do you know when you have found all the prime factors?
If all the factors are prime numbers and they total the original number, you have found them all. All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.
