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To determine how many of the first 250 triangular numbers are divisible by 5, we first note that the (n)-th triangular number is given by the formula (T_n = \frac{n(n+1)}{2}). A triangular number is divisible by 5 if either (n) or (n+1) is divisible by 10 (since one of them will be even, ensuring that the division by 2 does not affect divisibility). Among the first 250 integers, there are 50 multiples of 5 (for (n)) and 25 multiples of 10 (for (n+1)). Thus, there are (50 + 25 = 75) triangular numbers that are divisible by 5.
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How many numbers in the first 200 natural numbers are divisible by 6 or 8?
50 of them.
How many 5 digit numbers are divisible by 150?
There are 600 5-digit numbers divisible by 150.
What are the first ten triangular numbers?
The first ten triangular numbers are calculated by the formula ( T_n = \frac{n(n + 1)}{2} ), where ( n ) is a positive integer. The first ten triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, and 55. Each number represents the total number of dots that can form an equilateral triangle with that many rows.
How many prime numbers divisible by three?
No prime numbers are divisible by 3. By definition a prime number isn't divisible by anything but itself and 1.
How many numbers is 625 divisible by?
625 is divisible by these five numbers: 1, 5, 25, 125, 625.
How many numbers in the first 200 natural numbers are divisible by 6 or 8?
50 of them.
How many numbers between 1 and 100 are divisible by 3 or 7?
Oh, what a lovely question! Let's see, we can find the numbers divisible by 3 first, which are 33 numbers, and the numbers divisible by 7, which are 14 numbers. But wait, some numbers are divisible by both 3 and 7, so we must be careful not to count them twice. In the end, there are 47 numbers between 1 and 100 that are divisible by 3 or 7. Happy counting!
How many triangular numbers are also square numbers?
There are an many triangular numbers that are also square numbers. Simply put, the sum of two consecutive triangular number equals a square number. Examples include 1 and 36.
What numbers are not divisible by 600?
The lists of numbers divisible by and not divisible by 600 are both infinite.
How many numbers are not divisible by 2?
all odd numbers, which are infinite, are not divisible by two.
How many numbers between 1 and 600 are divisible by 2 and 3?
between 1 and 600 inclusive there are:300 numbers divisible by 2200 numbers divisible by 3100 numbers divisible by both 2 and 3400 numbers divisible by 2 or 3.
What are the divisible numbers of 2?
All real numbers are divisible by 2. Only the even numbers (there are infinitely many) are divisible by 2 without remainder.
How many numbers between 1 and 100 inclusive are divisible by 9 or 4?
To find the numbers between 1 and 100 inclusive that are divisible by either 9 or 4, we first determine how many numbers are divisible by 9 and how many are divisible by 4. There are 11 numbers divisible by 9 (9, 18, 27, ..., 99) and 25 numbers divisible by 4 (4, 8, 12, ..., 100). However, we must be careful not to double-count numbers divisible by both 9 and 4 (36, 72). Therefore, the total number of numbers divisible by 9 or 4 between 1 and 100 inclusive is 11 + 25 - 2 = 34.
How many numbers are divisible by 9 between 5 and 1000?
111 numbers between 5 and 1000 are divisible by 9
How many two - digit numbers are divisible by 3?
Oh, isn't that a happy little question! To find the two-digit numbers divisible by 3, we start by finding the first two-digit number divisible by 3, which is 12. Then, we find the last two-digit number divisible by 3, which is 99. Now, we can count how many numbers there are between 12 and 99 that are divisible by 3.
How many 5 digit numbers are divisible by 150?
There are 600 5-digit numbers divisible by 150.
How many prime numbers divisible by three?
No prime numbers are divisible by 3. By definition a prime number isn't divisible by anything but itself and 1.
