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If you know the prime factorization of a number, you can predict how many factors it has. Add 1 to each exponent of each prime factor and multiply. The product will be the number of factors.
Example: The prime factorization of 30 is 2 x 3 x 5
Each of those factors has an implied exponent of 1. Add 1 to each and multiply.
2 x 2 x 2 = 8
30 has eight factors.
Half of them will be less than the square root, half will be greater.
The square root of 30 is between 5 and 6.
By the rules of divisibility, you know that 30 is divisible by 1 (because everything is), 2 (because it's even), 3 ( because its digits add up to a multiple of 3), and 5 (because it ends in 0)
Dividing those numbers into 30 gives you 30, 15, 10 and 6
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
That's how you know you got them all.
Wiki User
∙ 9y ago
Wiki User
∙ 9y agoUse a systematic approach. For fairly small numbers, you can try division by each number, up to the specified number. But for larger numbers, it is better to factor the number into prime factors. All the factors of the number are the different combinations of the number itself. For example, 28 is equal to 2 squared times 7; so you can use the "2" zero, one, or two times as a factor; you can also use the "7" either zero or one times as a factor; so in total, you have 8 factors (those include the trivial factors, i.e., 1, and the number itself).
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How do you know when you have found the longest possible sting factors of a number?
All of the factors are prime.
How can finding factor pairs help with finding all of the factors number?
If you know the prime factorization of a number, you can find out the total number of factors. Example: 210 2^1 x 3^1 x 5^1 x 7^1 = 210 Add one to the exponents and multiply them. 2 x 2 x 2 x 2 = 16, the total number of factors.
How do you know when you have found the longest factor string for a number?
All of the factors are prime.
What are the factors of 34 and how do you know its all the factors?
If you know the prime factorization of a number, you can find out the total number of factors. The prime factorization of 34 is 2^1 x 17^1 Add one to each exponent and multiply them. 2 x 2 = 4 34 has four factors. You already know about 2 and 17. The other two (like all numbers) are one and the number itself. 1, 2, 17, 34
What factor is not a factor of 66?
To find the factors that are not factors, find the factors of the number. All numbers that are not listed are not factors. 66: 1 x 66 2 x 33 3 x 22 6 x 11 The factors are 1, 2, 3, 6, 11, 22, 33, and 66. All other numbers are not factors of 66.
Why does number 25 have a odd number of factors?
Because it's a square number. All perfect squares have an odd number of factors because they have one factor pair that is the same number twice (the square root) and when the factors are listed, the number is listed once.
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
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.
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'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.
Why do all non square numbers have even factors?
The factors of all numbers can be written in pairs. With square numbers, one of those pairs is the same number twice. When listed singly, square numbers have an odd number of factors. All others are even.
How do you know when you have found the longest possible sting factors of a number?
All of the factors are prime.
What are all the prime factorizations?
You cannot list all the potential prime factors. Any prime number can be a prime factor. There are an infinite number of prime numbers, so there are an infinite number of potential prime factors. If given a specific number, the prime factors for it can be listed.
How can finding factor pairs help with finding all of the factors number?
If you know the prime factorization of a number, you can find out the total number of factors. Example: 210 2^1 x 3^1 x 5^1 x 7^1 = 210 Add one to the exponents and multiply them. 2 x 2 x 2 x 2 = 16, the total number of factors.
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.
What is the prime number 18 27 7 15?
7 is the prime number. All the other numbers listed have factors other than 1 and itself.
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.
