Factors l KHURRAM SHEHZAD MUGHAL l URDU l HINDI

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used. Example: Let us consider the number 8. 8 can be a product of 1 and 8, and 2 and 4. As a result, the factors of 8 are 1, 2, 4, 8. Therefore, when finding or solving problems involving factors, only positive numbers, whole numbers, and non-fractional numbers are considered. What is Factor? [Definition Facts & Example A general formula to remember is that a and b are factors of ab’s product. 2 ✕ 3 = 6. Therefore, 2 and 3 are factors of 6. There is no remainder when 6 is divided by either 2 or 3. 9 ✕ 3 = 27. Therefore, 9 and 3 are factors of 27. There is no remainder when 27 is divided by either 9 or 3. 7 ✕ 5 = 35. Therefore, 5 and 7 are factors of 35. There is no remainder when 35 is divided by either 5 or 7. Example: Find all the factors of the number 10. Factors of Numbers Properties of Factors All integers have a finite number of factors. A number’s factor is always less than or equal to the number; it can never be bigger than the number. Except for 0 and 1, every integer has a minimum of two factors: 1 and the number itself. Factors are found by employing division and multiplication. Fun Facts about Factors Factors are never decimals or fractions; they are only whole numbers or integers. All even numbers have 2 as a factor. 5 is a factor for all numbers that end in 0 and 5. All numbers higher than 0 and ending in a 0 have 2, 5, and 10 as factors. Factoring is a common way to solve or simplify algebraic expressions. Prime Factorization When we write a number as a product of all its prime factors, it is called prime factorization. Every number in prime factorization is a prime number. To write the number as a product of prime factors, sometimes we might have to repeat the factors too. Example: To write the prime factorization of 8, we can write 8 = 2 ✕ 2 ✕ 2, i.e, the prime factor 2 is repeated three times.