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.
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 work out the multiples of it which are only divisable by 1 and themselves.
Somewhere in front of you was a list of numbers. The instructions were asking you to break down the numbers and write them as a product of their prime factors. This is known as the prime factorization. The prime factorization of 30 is 2 x 3 x 5.
That's an infinite list. Numbers with three factors are the squares of prime numbers.
Usually, but not necessarily and not if they're prime. All prime numbers have the same number of factors.
All prime numbers have only two factors. 2, 3, 5, 7, 11
All of them. Different numbers have different numbers of factors.
List all the factors. Select the ones that are prime numbers.
All numbers have factors. Some factors are prime numbers. A prime factor is a factor that is a prime number. A common prime factor is a prime factor that appears on the list of factors of two or more given numbers.
2,3,5
Prime numbers never stop, it is impossible to list them all.
2 and 5 are the prime factors of 100.
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.
All numbers have factors. Some factors are prime numbers. These are known as prime factors.
Somewhere in front of you was a list of numbers. The instructions were asking you to break down the numbers and write them as a product of their prime factors. This is known as the prime factorization. The prime factorization of 30 is 2 x 3 x 5.
That's an infinite list. Numbers with three factors are the squares of prime numbers.
Yes, all prime numbers have only two factors
All prime numbers have two factors.
do the prime factorization of the 3 numbers. list the prime factors of all the 3 numbers. circle the factors that are common to the 3. multiply them. that number is the HCF