Divisibility rule is a way of finding whether a number is completely divisible by another number or not without actually dividing the number. In this problem, we have used the divisibility rule to find the numbers. These numbers are the prime numbers between the numbers 50 and 100. We will eliminate these from the remaining numbers. Hence, the numbers 77 and 91 are divisible by 7. To check divisibility by 7, twice the unit’s place digit subtracted from the rest of the number should be divisible by 7.įor example, we observe that \ Now, we check the divisibility of the number by 7. Hence, we remove these numbers from our answer. The number is divisible by 3 if the sum of digits is divisible by 3. We sum up the digits of the remaining numbers. Next, let us check the divisibility of these numbers by 3. Hence, we can eliminate the numbers 55, 65, 75, 85, 95 from our answer. Hence, we can eliminate the numbers 50, 54, 56, 58, …, 94, 96, 98, 100 from our answer.Īll numbers that end with the digit 0 or 5 are divisible by 5. Thus, all numbers divisible by 2 (except 2 itself) are composite numbers. We know that all even numbers are divisible by 2. We will use divisibility rules to easily identify the composite numbers between 50 and 100, and then eliminate them from our answer. They are divisible by at least one more factor other than 1 and themselves. Hence, it is obvious that they will be divisible by 1 and the number itself.Ĭomposite numbers are the numbers which are not prime numbers. We know that in the number system, prime numbers are the numbers which have only two factors, 1 and the number itself. A composite number is a number which is not a prime number, that is it is divisible by 1, itself, and some other numbers as well. A prime number is a number divisible by only 1 and itself. It will not ask you to figure out whether numbers greater than 100 are prime.Here, we will be using the various divisibility rules to easily identify the numbers that are not prime, and eliminating them from our answer. The GMAT occasionally will have questions that require you to figure out whether larger two-digit numbers are prime. For example, the next year that will be a multiple of 9 is 2016, because 2 + 0 + 1 + 6 = 9. That pattern also works with 9 - if the sum of the digits is divisible by 9, then the original number is divisible by 9. Consider the number 2012 - 2 + 0 + 1 + 2 = 5, which is not divisible by 3, so that means 2012 is not divisible by 3. For example, consider the number 285 - 2 + 8 + 5 = 15, which is divisible by 3, so that means 285 must be divisible by 3. If the sum of the digits is divisible by 3, then the original number is divisible by 3. The rule for 3 is a bit different from the rules for other numbers. 2 or 6, the one-digit even numbers that are not multiples of 4 – and the tens digit is odd, then the number is divisible by 4. If the last digit is even but not one of those - viz. If the last digit is 0, 4, or 8, and the tens digit is even, then the number is divisible by 4. Think of the one-digit numbers that are multiples of 4: those are 0, 4, and 8. A two digit number in which the first and last digits are the same is divisible by 11. A number that ends with a 5 or a 0 is divisible by 5.