A number is a basic element of Mathematics. It is a very important constituent of day to day calculations which can be used to count, measure and label things and objects. According to the fundamental law of arithmetic, every number can be expressed as a product of their primes. Prime numbers are those numbers which have only two factors and the two factors are one and the number itself. The factors of 215 can be determined by various methods such as prime factorization method and factor tree method.
Factors of 215 = 1, 5, 43, -1, -5, -43, 215, -215
Prime factorization is a method of finding the factors of a number by dividing it by prime numbers. Prime factorization of 215 is done as follows.
Step 1: Check for the lowest prime number that can divide 215. The lowest prime number is 2. But 215 is not a multiple of 2. The next lowest prime number is 3. However, 3 also does not divide 215 The next prime number is 5. 215 is a multiple of 5. When 215 is divided by 5, the quotient obtained is 43. So ‘5’ is one of the prime factors of 215.
Step 2: The quotient obtained in step 1 is further simplified into prime factors. However, in case of 215, the quotient obtained in step 1 is 43. This number is a prime number and has only two factors (43 and 1) i.e. The number can only be divided by 43 and 1.
Step 3: The number 215 is now expressed as a product of its prime factors. The prime factors of 215 are 5, 43 and 1. So, 215 = 5 x 43 x 1.
So, the factors of 215 are 1, 5 and 43.
A factor tree is a diagrammatic representation of all the prime factors of a number. Factor tree helps in easy and effective representation of a number. It helps us understand the concept of factorization in an efficient manner. The division of numbers by its prime factors is represented in the form of an hierarchical tree. The factor tree representation of prime factorization of 215 is depicted in the figure below.
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Steps to construct the factor tree for 215:
Step 1: 215 is written within a circular or a rectangular box..
Step 2: The number 215 is branched to two circles: one representing the lowest prime number which can divide 215 and the other circle represents the quotient obtained after dividing 215 by the lowest prime number.
Step 3: The quotient obtained in step 2 is further divided into its prime factors. The branching continues till further division is not possible. i.e. till 1 is obtained as a factor in each split.
By finding the prime factors of a number, we can analyse a few properties about that number. The prime factorization of 215 indicates all the prime factors of 215. The factors of 215 are 1, 5 and 43. By this, we can determine its characteristics.
215 is a composite number and it satisfies the fundamental theorem of arithmetic because it can be expressed as a product of its prime factors as 1 × 5 × 43.
215 is not a perfect square number. This is because 215 does not have pairs of identical factors. If the number has pairs of identical factors and no factor is left out from the pair, then such a number is a perfect square number.
215 is not a perfect cube number. This is because 215 does not have the prime factors which repeat thrice.
215 is not an even number because it does not have the prime number ‘2’ as one of its factors. Hence it is an odd number.
215 may also have negative factors like -1, -5, -43 etc.
Factors of a number reveal several characteristics of that number.
There are several pair factors of 215. The positive pair factors of 215 are (1, 215) and (5, 43) and the negative pair factors of 215 are (-1, -215) and (-5, - 43). Since 215 cannot be expressed as pair factors of identical factors, it is not a square number.
1. What are Common Factors?
Factors are the numbers which are multiplied to get the other numbers. A number may have positive and negative factors. Common factors are always found between the two or more numbers. If two or more numbers are factorized and found that they have few factors in common, these factors that are the same for a set of numbers is called a common factor. For example, all the even numbers have 2 as a common factor. Even integers may also have -2 as a common factor. Common factors are different from common multiples.
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