Solution In this question, we are explicitly asked to calculate the prime factors of 85 and 80. Example 2 Use the prime factorization method to find out the prime factors of 80 and 85, then separate the factors of both into prime and composite numbers. Similarly, 1 is the smallest common factor between 85 and 40. Among 1 and 5, we can quickly point out that 5 is the highest common factor between 85 and 40. To find out the highest common factor, let us first write down the common factors between the two. Solution The factors 85 and 40 can be found through the division method, and these factors are: The factors of 85 are: Factors of 85 are the following: 1, 5, 17, and 85. Also, find out the highest and smallest common factor between them. Example 1 Write down the factors of 85 and 40. To find out the factor pairs:ĥ x 17 = 85 These are the positive factor pairs of 85: Factor pairs of 85 = (1, 85), (5, 17) Without any significant changes in the numbers, the negative factor pairs are positive factor pairs but with an inverted sign which means that positive (+) is changed to negative (-): Negative factor pairs of 85 = (-1, -85), (-5, -17) Factors of 85 Solved Examples Here are some examples that have been solved to provide an idea of how to go about factoring numbers. First, recall the factors of 85: Factors of 85 are the following: 1, 5, 17, and 85. ![]() The condition is that when these two factors are multiplied by each other, they must produce an answer that is equal to the original number of which the factors were calculated. Not any couple of random factors can make a factor pair of 85 there exists a necessary condition that has to be fulfilled. Prime factorization of 85 = 5 x 17 Using the figure attached below, you can visually understand how we went about this method:įigure 3 – Factor Tree of 85 Factors of 85 in Pairs All factor pairs of 85 are essentially a pair of its factors written down between round brackets “()” and separated by a comma. Therefore, the prime factorization equation of 85 is: We stopped here because dividing 17 by 17 gave us 1, and no further division is possible at this stage. The reason behind 17 not being divisible by 7 is because 17 itself is a prime number and is only divided completely by 1 and 17 itself, so:ġ7 $\div$ 17 = 1 Hence, both 5 and 17 are the prime factors of 85. Moving on, the next prime number after 5 is 7, but 17, as we know, is not divisible by 7. How this is done is explained in detail in this section: We find out the first prime number, which will divide 85 completely and evenly this prime number turns out to be 5Ĩ5 $\div$ 5 = 17 Usually, we start from 2, which is also a prime number, but 85 is an odd number, so we know that 85 would not be divisible by 2. This division involves constant changing of the divisor and the dividend. As we can observe, the division operation is also used in prime factorization but is not the same division we perform in basic calculations of mathematical numbers. The prime numbers which divide 85 ultimately and evenly are called prime factors. Prime factors are obtained by dividing 85 with prime numbers only. Factors of 85 by Prime Factorization The factors of 85 calculated through prime factorization are called prime factors. Using this method, we find out the following factors of 85: Factors of 85 through division method: 1, 5, 17, and 85. This approach is shown in the steps below: \ 1 is also a factor of 85. We continue this process until we reach the possible range identified for the factors. After identifying whether a number is even or odd, we start from 2 by dividing 85 by it to find whether it divides the number completely. ![]() As we discussed earlier, the division method is a straightforward approach to finding out the factors of 85. ![]() Before getting into any other method, we will first look at the division method. Another method is the prime factorization of 85, which only gives the prime factors of 85 this method is visually represented and drawn through a factor tree diagram. Numbers that divide 85 are entirely considered factors of it. The division method is essentially based on finding factors of 85 through complete and even division. How To Calculate the Factors of 85? The factors of 85 are easy to calculate through tools such as the division method. The number 85 is an odd composite number, so the factors it has are both prime and composite numbers. 85 has only four factors, so that they can be divided into two positive factor pairs and two negative factors. What Are the Factors of 85? The factors of 85 are the following: 1, 5, 17, and 85. Figure 1 – All possible Factors of 85 We will also show solved examples in the last section to make the lesson clear and comprehensive.
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