![]() ![]() Then, all the prime factors that are divisors are multiplied. This step is repeated until the quotient becomes 1. After this, the quotient is again divided by the smallest prime number. Division method - In this method, the given number is divided by the smallest prime number which divides it completely.Prime factorization of any number can be done by using two methods: Here 2 and 3 are the prime factors of 18. For example, the prime factorization of 18 = 2 × 3 × 3. A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of any number means to represent that number as a product of prime numbers. Thus, HCF of (850, 680) = 170, LCM of (850, 680) = 3400įAQs on Prime Factorization What is Prime Factorization in Math?.LCM is the product of the common prime factors with the highest powers.HCF is the product of the common prime factors with the smallest powers.Observing this, we can see that the common prime factors of 850 and 680 with the smallest powers are 2 1, 5 1 and 17 1, and the common prime factors with the highest powers are 2 3, 5 2, 17 1.The prime factorization of 680 is: 680 = 2 3 × 5 1 × 17 1.The prime factorization of 850 is: 850 = 2 1 × 5 2 × 17 1.Solution: We will first do the prime factorization of both the numbers. LCM is the product of the common prime factors with the highest powersĮxample: What is the HCF and LCM of 850 and 680?.The following points related to HCF and LCM need to be kept in mind: For this, we first do the prime factorization of both the numbers. To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers, we use the prime factorization method. Prime factorization plays an important role for the coders who create a unique code using numbers which is not too heavy for computers to store or process quickly. The two most important applications of prime factorization are given below.Ĭryptography is a method of protecting information using codes. Prime factorization is used extensively in the real world. Therefore, the prime factors of 60 are 2, 3, and 5. Prime factorization of 60 = 2 × 2 × 3 × 5 Step 4: Finally, multiply all the prime factors that are the divisors.Since we get 1 as the quotient, we stop here. Now, 15 is not divisible by 2, so we take the next prime number which is 3. Step 3: Repeat step 2, until the quotient becomes 1.So, 30 is again divided by 2 and we get 15. Step 2: Again, divide the quotient of step 1 by the smallest prime number.Step 1: Divide the number by the smallest prime number such that the smallest prime number should divide the number completely.Let us learn how to find the prime factors of a number by the division method using the following example.Įxample: Do the prime factorization of 60 with the division method. The division method can also be used to find the prime factors of a large number by dividing the number by prime numbers. So, we get the prime factors of 850 = 2 × 5 2 × 17 Step 4: Repeat step 3, until we get the prime factors of all the composite factors.Here, 25 can be further factorized into 5 × 5, and 34 can be factorized into 17 × 2 Step 3: Factorize the composite factors that are found in step 2, and write down the pair of factors as the next branches of the tree.Step 2: Then, write down the corresponding pair of factors as the branches of the tree.Step 1: Place the number, 850, on top of the factor tree.Solution: Let us get the prime factors of 850 using the factor tree given below. Let us understand the prime factorization of a number using the factor tree method with the help of the following example.Įxample: Do the prime factorization of 850 using the factor tree. In the factor tree method, the factors of a number are found and then those numbers are further factorized until we reach the prime numbers. Prime Factorization by Factor Tree Method Prime factorization by factor tree method. ![]() The most common methods that are used for prime factorization are given below: ![]() There are various methods for the prime factorization of a number. ![]()
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