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How many are the first 100 positive integers are divisible by 7?
(7*100*101)/2 = 35,350 jpacs * * * * * What? How can there be 35,350 integers in the first 100 integers? There are 14 of them.
What is the smallest integer that is divisible by the first 10 positive integers?
The smallest integer that is divisible by the first 10 positive integers (1 through 10) is known as the least common multiple (LCM) of those numbers. The LCM of 1 through 10 is 2520. This is found by taking the highest powers of all prime factors present in the factorizations of these integers. Thus, 2520 is the smallest integer divisible by all of them.
How many positive integers less than 1001 are divisible by either 2 or 5 or both?
To find the number of positive integers less than 1001 that are divisible by either 2 or 5, we use the principle of inclusion-exclusion. First, the count of integers divisible by 2 is ( \left\lfloor \frac{1000}{2} \right\rfloor = 500 ), and those divisible by 5 is ( \left\lfloor \frac{1000}{5} \right\rfloor = 200 ). The count of integers divisible by both 2 and 5 (i.e., by 10) is ( \left\lfloor \frac{1000}{10} \right\rfloor = 100 ). Thus, the total is ( 500 + 200 - 100 = 600 ). Therefore, there are 600 positive integers less than 1001 that are divisible by either 2 or 5.
How many positive integers less than 100 are divisible-by 3 5 and 7?
To find how many positive integers less than 100 are divisible by 3, 5, and 7, we first calculate their least common multiple (LCM). The LCM of 3, 5, and 7 is 105. Since 105 is greater than 100, there are no positive integers less than 100 that are divisible by all three numbers. Therefore, the answer is 0.
How many positive integers less than 30 are divisible 2 but not by 3?
To find the positive integers less than 30 that are divisible by 2 but not by 3, we first determine the integers divisible by 2. These are 2, 4, 6, ..., 28, which gives us 14 numbers (2 times each integer from 1 to 14). Next, we identify those among them that are also divisible by 3: 6, 12, 18, and 24, totaling 4 numbers. Therefore, the count of integers divisible by 2 but not by 3 is 14 - 4 = 10.
How many are the first 100 positive integers are divisible by 7?
(7*100*101)/2 = 35,350 jpacs * * * * * What? How can there be 35,350 integers in the first 100 integers? There are 14 of them.
Define prime numbers?
A prime number is a number in the set of positive integers such that it is only divisible by 2 unique numbers: itself, and 1. For this reason the first prime number is 2, not 1.
What is the total number of integers between 100 and 300 that are divisible by 3?
To find the total number of integers between 100 and 300 that are divisible by 3, we first determine the smallest and largest integers in this range that are divisible by 3. The smallest integer divisible by 3 is 102, and the largest is 297. To find the total number of integers between 102 and 297 that are divisible by 3, we calculate (297-102)/3 + 1, which equals 66. Therefore, there are 66 integers between 100 and 300 that are divisible by 3.
What is the smallest integer that is divisible by the first 10 positive integers?
The smallest integer that is divisible by the first 10 positive integers (1 through 10) is known as the least common multiple (LCM) of those numbers. The LCM of 1 through 10 is 2520. This is found by taking the highest powers of all prime factors present in the factorizations of these integers. Thus, 2520 is the smallest integer divisible by all of them.
How many positive integers less than 1001 are divisible by either 2 or 5 or both?
To find the number of positive integers less than 1001 that are divisible by either 2 or 5, we use the principle of inclusion-exclusion. First, the count of integers divisible by 2 is ( \left\lfloor \frac{1000}{2} \right\rfloor = 500 ), and those divisible by 5 is ( \left\lfloor \frac{1000}{5} \right\rfloor = 200 ). The count of integers divisible by both 2 and 5 (i.e., by 10) is ( \left\lfloor \frac{1000}{10} \right\rfloor = 100 ). Thus, the total is ( 500 + 200 - 100 = 600 ). Therefore, there are 600 positive integers less than 1001 that are divisible by either 2 or 5.
What is a 6 digit number divisible by the first 10 integers?
362880 is one possibility.
How many positive integers less than 100 are divisible-by 3 5 and 7?
To find how many positive integers less than 100 are divisible by 3, 5, and 7, we first calculate their least common multiple (LCM). The LCM of 3, 5, and 7 is 105. Since 105 is greater than 100, there are no positive integers less than 100 that are divisible by all three numbers. Therefore, the answer is 0.
How many positive integers less than 30 are divisible 2 but not by 3?
To find the positive integers less than 30 that are divisible by 2 but not by 3, we first determine the integers divisible by 2. These are 2, 4, 6, ..., 28, which gives us 14 numbers (2 times each integer from 1 to 14). Next, we identify those among them that are also divisible by 3: 6, 12, 18, and 24, totaling 4 numbers. Therefore, the count of integers divisible by 2 but not by 3 is 14 - 4 = 10.
Which is the first positive number divisible by 1 2or 3?
6 is the first number that's divisible by any one of those digits, or all three.
What is the sum of the first 30 positive integers?
The sum of the first 30 positive integers is: 465.
What is the sum of the first ten positive integers?
The sum of the first ten positive integers is: 55
What is the sum of the first 500 positive integers?
The sum of the first 500 positive integers is: 125,250
