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In the end you have 1, 3 and 9 as a list of factors. (ii) Inside the square root, for every two same numbers multiplied, one number can be taken out of the square root. It is determined that the prime factors of number 9216 are: 2, 3. In this case, 9216 can be written as 2^10 * 3^2. Factor 9216 into its prime factors 9216 = 2 10 • 3 2 To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent. Because all numbers have a minimum of two factors(one and itself). The prime factors of 9216 are 2 and 3. (viii) 9216 By prime Factorization, 9216 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 How do you calculate natural number factors? In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 x 5, and the polynomial x2 - 4 factors as (x - 2)(x + 2). Equcation for number 9216 factorization is: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 It is determined that the prime factors of number 9216 are: 2, 3 Prime Factorization Of 9215 Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Prime numbers or primes are natural numbers greater than 1 that are only divisible by 1 and with itself. USING OUR SERVICES YOU AGREE TO OUR USE OF. This site is best viewed with Javascript. Factor 9216 into its prime factors 9216 = 210 • 32 To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.Factors which will be extracted are : 9216 = 210 • 32 No factors remain inside the root ! For example 7 has two factors 1 and 7. (iii) Combine the like square root terms using mathematical operations. Prime factorization is when you write a number in simplest form by multiplying all of its prime factors together. The prime factorization of 9216 = 2 10 •3 2. Let's create an example for factorization with the number nine. Thew following steps will be useful to find square root of a number by prime factorization. No the number 9216 is not a prime number. The number of primes is infinite. To get the number that you are factoring just multiply whatever number in the set of whole numbers with another in the same set. Nine thousand, two hundred and sixteen is a. It's not dividable by 2 evenly that's why we skip it(Remembe 4,5 so you know when to stop later). In all cases, a product of simpler objects is obtained. All numbers without remainders are factors including the divider itself. Number 6 has four factors 1, 2, 3 and 6 itself. Work your way up until you arrive to 5 (9 divided by 2, rounded up). It is simple to factor numbers in a natural numbers set. Find the square roots of the following numbers by the Prime Factorization Method: (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100. Factors which will be extracted are : 9216 = 2 10 • 3 2 No factors remain inside the root !! If you are unable to turn on Javascript, please click here. !To complete the simplification we take the squre root of the factors which are to be extracted. Answer: (i) 729 The prime factorization of 729 is \[729=3\times 3\times 3\times 3\times 3\times 3\]. For finding other factors you will start to divide the number starting from 2 and keep on going with dividers increasing until reaching the number that was divided by 2 in the beginning. This deals with simplifying square roots. 96. Natural numbers bigger than 1 that are not prime numbers are called composite numbers. We do this by dividing their exponents by 2 : 96 = 25 • 3 The simplified SQRT looks like this: 96. 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