Power of 2 in 72 = 3, and power of 2 in 300 = 2,.Step 3: Find the power of each of these prime factors, which is the greatest between both the numbers. Thus, distinct prime factors from both combined are 2, 3 and 5.Step 2: List down all the distinct prime factors from both the numbers Step 1: Represent the two given numbers in their prime factorization form Let us consider two positive integers, 72 and 300 Now that we know what is an LCM and GCD, let us learn a method to find the LCM and GCD of any two given positive integers. Method to find LCM and GCD of any two given positive integers Let us first learn what is a factor or divisor, and then we can learn about GCD or HCF.įactor/Divisor: If the remainder when a number “N” is divided by another number “n” is zero, then n is said to be a factor or divisor of N.Īnd, HCF or GCD is the largest common factor/divisor to any two or more given positive integers.įor example: The GCD of 24 and 30 is 6, since 6 is the greatest number, which is a factor of both 24 and 30. Multiple: If the remainder when a number “N” is divided by another number “n” is zero, then N is said to be a multiple of n.Īnd, LCM is the smallest common multiple of any two or more given positive integers.įor example: LCM of 4 and 6 is 12, since 12 is the smallest number, which is a multiple of both 4 and 6 Properties of numbers: Highest Common Factor or Greatest Common Divisor (HCF/GCD) Properties of numbers: Least Common Multiple (LCM)īefore we see what an LCM is, let us understand the meaning of a multiple. Now, let us learn a few more properties of numbers where we apply prime factorization. We already know that any given positive integer can be expressed as a product of one or more prime numbers. We are the most reviewed online GMAT Prep company with 2400+ reviews on GMATClub.Ĭreate your Personalized Study Plan Prime factorization Ace GMAT Quant by signing up for our free trial and get access to 400+ questions. Questions on Number Properties are very commonly asked on the GMAT. Step 5: If yes then the given number is not a prime number, else it is a prime number We need not check for other prime numbers.Step 4: Check whether any of these prime numbers can divide the given number or not Prime numbers less than or equal to 11 are 2, 3, 5, 7, and 11.Step 3: List down all the prime numbers which are less or equal to this integer Step 2: Round it off to the closest integer The square root of 123 approximately equal to 11 as 11 2 = 121.Step 1: Find the square root of the given number Let’s say the number is 123, can we quickly find whether 123 is prime or not?įor this, let us learn a five-step approach to check whether a given number is a prime number or not?.It is easy to check whether a single-digit or a two-digit number is prime or not, but what if we are given a three-digit number or more. So, we know what is a prime number, but how do we check whether a given number is prime or not? What is the process to check whether a given number is prime or not? Every positive integer can be expressed as a product of one or more prime numbersĮxample: 55 = 5 * 11, where 5 and 11 are two prime numbersīased on the above definition, Is 1 a prime number?.Note: 2 is the only prime number, which is even, because all other even numbers will be divisible by at least three numbers, 1, 2 and the number itself. A number which is divisible by only two number, 1 and the number itself, is called a prime number.Properties of Numbers: Prime Numbers Definition Now that we know what are even and odd numbers, let’s see their properties. Note: There is an odd number between every two consecutive even numbers.Īccording to the definitions given above is 0 an even or an odd number? Properties of numbers: Even and Odd number properties So, all integers that end with 1, 3, 5, 7 or 9 are odd numbersĮxample: 7, 31, 75, 499 are all odd numbers.So, any integer which is in the form of 2k ± 1, where k is an integer, is an odd number.Or, in other words, an integer that is not a multiple of 2 is an odd number.Any integer which is not an even number is an odd number.So, all integers that end with 0, 2, 4, 6 or 8 are even numbersĮ×ample: 4, 56, 98, 200 are all even numbers Odd Numbers.So, any integer which is in the form of 2k, where k is an integer, is an even number.Any integer that is a multiple of 2 is an even number.Properties of numbers: Even – Odd Even Numbers You will also get to know a few facts about the properties of the numbers.You will get a deeper idea about the behavior of numbers and its operations. ![]() We see that you want to know the basics and properties of numbers.
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