What do prime factorization

Prime factorization is the way of writing a number as the multiple of their prime factors. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. The prime factorization of 72, 36, and 45 are shown below.

The least common multiple of a number is the smallest number that is the product of two or more numbers. LCM of two numbers can be found out by first finding out the prime factors of the numbers. Then the LCM is the product of the greatest power of each common prime factor. HCF of two numbers can be found out by first finding out the prime factors of the numbers. Then the HCF is the highest common factor from the prime factors of the two numbers.

It is widely used in cryptography as the study of secret codes is known as cryptography. Prime numbers are used to form or decode those codes. Learn Practice Download. What is Prime Factorization? Prime Factorization of a Number 3. What are Factors and Prime Factors?

Methods to Find the Prime Factorization 5. Applications of Prime Factorization 6. Great learning in high school using simple cues. Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes. FAQs on Prime Factorization. What is Prime Factorization in Math?

How to Find Prime Factorization? Prime factorization of any number can be calculated out by following two methods: Method 1: Division method. Method 2: Factor tree method. What is the Prime Factorization of 72, 36, and 45? Where is Prime Factorization Useful? What is the Prime Factorization of 24? We could keep going. I think you get the general idea. You move to 7, 7 is prime.

It's only divisible by 1 and 7. Prime is not the same thing as odd numbers. Then if you move to 10, 10 is also not prime, divisible by 2 and 5. And we could keep going on like this. People have written computer programs looking for the highest prime and all of that. So now that we know what a prime is, a prime factorization is breaking up a number, like 75, into a product of prime numbers. So let's try to do that. So we're going to start with 75, and I'm going to do it using what we call a factorization tree.

So we first try to find just the smallest prime number that will go into Now, the smallest prime number is 2. Does 2 go into 75? Well, 75 is an odd number, or the number in the ones place, this 5, is an odd number.

So then we could try 3. Does 3 go into 75? Well, 7 plus 5 is So 75 is 3 times something else. And if you've ever dealt with change, you know that if you have three quarters, you have 75 cents, or if you have 3 times 25, you have So this is 3 times Write the number 91 on the board. Finding the prime factorization of numbers will strengthen your students' basic facts and understanding of multiplication.

Students who do not know their basic multiplication facts will likely struggle with this, because they do not recognize products such as 24 or 63 readily. Turning the problem around and giving them the prime factorization of a number and asking them what they know about the number without multiplying it out is a good way to assess their understanding of the divisibility rules, the concept of factoring, and multiplication in general. To develop students' conceptual understanding and help them grow into procedurally fluent mathematicians, explore HMH Into Math , our core solution for K—8 math instruction.

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Sign In. Cart 0. My Account. Tweet Tweet Share. Key standard: Determine whether a given number is prime or composite, and find all factors for a whole number. Writing a Product of Prime Factors When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. Examine the two factor trees for 72 shown below. Introducing the Concept: Finding Prime Factors Making sure your students' work is neat and orderly will help prevent them from losing factors when constructing factor trees.

Write the number 48 on the board. Ask : Who can give me two numbers whose product is 48? Students should identify pairs of numbers like 6 and 8, 4 and 12, or 3 and Take one of the pairs of factors and create a factor tree for the prime factorization of 48 where all students can see it. Ask : How many factors of two are there? If they don't, remind them that the exponent tells how many times the base is taken as a factor. Next, find the prime factorization for 48 using a different set of factors.

Ask: What do you notice about the prime factorization of 48 for this set of factors? Say : There is a theorem in mathematics that says when we factor a number into a product of prime numbers, it can only be done one way, not counting the order of the factors.

Say : Now let's try one on your own. Find the prime factorization of 60 by creating a factor tree for Have all students independently factor As they complete their factorizations, observe what students do and take note of different approaches and visual representations.

Ask for a student volunteer to factor 60 for the entire class to see. Ask : Who factored 60 differently? Have students who factored 60 differently either by starting with different factors or by visually representing the factor tree differently show their work to the class. Ask students to describe similarities and differences in the factorizations. If no one used different factors, show the class a factorization that starts with a different set of factors for 60 and have students identify similarities and differences between your factor tree and other students'.

The students should say no, because 9 is not a prime number. If they don't, remind them that the prime factorization of a number means all the factors must be prime and 9 is not a prime number.