What is the value of the first triangle number to have over 500 divisors?

What is the value of the first triangle number to have over 500 divisors?

76,576,500
Want the first triangular number with the number of divisors to be more than 500. And the number, 76,576,500 (the 12375th triangular number) is indeed the first triangular number with more than 500 divisors.

Is 500 a triangular number?

List Of Triangular Numbers. 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, and so on.

What is the smallest triangular number after 100?

The triangular numbers up to 100 are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91 — so what’s next? Perfect Numbers These are the numbers which equal the sum of all of their smaller factors. They are few and far between — in fact, nobody knows how many there are. Only 47 perfect numbers are currently known.

Is the smallest triangular number?

The starting triangular numbers are 1, 3, 6, 10, 15, 21, 28………… Smallest triangular number with 2 digits = 10, and 4 is the index of 10. 3 digits = 105, and 14 is the index of 105.

How do you find triangular numbers in Python?

Settings

1. print(“Triangular Number Sequence – Finding the nth term. n\n”)
2. n = int(input(“Type a number between 1 and 1,000,000,000”
3. triangularNumber = int(n*(n+1)/2)
4. print(“The ” + str(n) + “th triangular number is: “

What is the HCF of 2 and 4?

As visible, 2 and 4 have only one common prime factor i.e. 2. Hence, the HCF of 2 and 4 is 2.

How to find the smallest number with 500 divisors?

First Step: Find the smallest number with 500 divisors. Seems like a good starting point to begin our search. Second Step: Starting at the number found in the previous step, search for the next triangle number. Check to see whether this number has 500+ divisors.

Which is the first triangle number to have over five hundred divisors?

We can see that 28 is the first triangle number to have over five divisors. What is the value of the first triangle number to have over five hundred divisors?

How to find a highly divisible triangular number?

Second Step: Starting at the number found in the previous step, search for the next triangle number. Check to see whether this number has 500+ divisors. If yes, this is the number we were looking for, else…

What’s the fourth step of the triangle equation?

Fourth Step: Add (n+1) to the last triangle number found, to find the next triangle number. Check whether this number has 500+ divisors. If yes, this number is the answer. If not, repeat Fourth Step till the process terminates. The First Step isn’t exactly a piece of cake, but necessary to reduce computation time.