There are not a lot of numbers that can be divided by all the numbers from 1 to 10, and 2520 is one of them. Picture for representationThere is a strange number that baffles mathematicians across the world. 2520 is a very
special number for many reasons. This number was discovered by Indian mathematicians with their unwavering intelligence. There are not a lot of numbers that can be divided by all the numbers from 1 to 10, and 2520 is one of them. But why is it considered special if there are other numbers that can be divided by all numbers from 1-10? Here are some reasons why 2520 is a special number: - 2520 is the smallest number that can exactly be divided by all integers
(whole numbers) from 1 to 10, whether even or odd. It also happens to be divisible by 12, but not 11.
2520 ÷ 1 = 2520
2520 ÷ 2 = 1260
2520 ÷ 3 = 840
2520 ÷ 4 = 630
2520 ÷ 5 = 504
2520 ÷ 6 = 420
2520 ÷ 7 = 360
2520 ÷ 8 = 315
2520 ÷ 9 = 280
2520 ÷ 10 = 252 - The secret of the number 2520 is hidden in the multiplication of [7 × 30 × 12]. With regard to the Indian Hindu year, the riddle of this 2520 number is solved, it is the coefficient of this number. Days of
the week (7), days of the month (30) And months in a year (12). [7 × 30 × 12 = 2520] This is the characteristic and dominance of time.
- These secrets about the number 2520 were discovered by the great Indian mathematician Sri Srinivasa Ramanujan.
- 2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.
- 2520 is the last highly composite number that is a divisor of all following highly composite numbers.
- Half of 7!
(5040), meaning 7 factorial, or 1×2×3×4×5×6×7.
- The product of five consecutive numbers, namely 3×4×5×6×7.
Topics
- Click here to see ALL problems on Divisibility and Prime Numbers
Question
557800: What is the smallest number that can be divided by all the numbers 1 to 10?
Answer by Edwin McCravy(19247) (Show Source): You can put this solution on YOUR website!
Let the number be N
1 = 1 so N must have factor 1 (every integer has factor 1, so we can ignore 1)
2 = 2 so N must have factor 2
3 = 3 so N must have factor 3
4 = 2*2 so N must have factor 2*2
5 = 5 so N must have factor 5
6 = 2*3 so N must have factor 2*3
7 = 7 so N must have factor 7
8 = 2*2*2 so N must have factor 2*2*2
9 = 3*3 so N must have factor 3*3
10 = 2*5 so N must have factor 2*5
So the smallest N can be and have at least as many of
every factor above is the product of three 2's, two 3's,
one 5, and one 7, which means
N = 2*2*2*3*3*5*7 = 2520
Edwin
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2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode
characters. Learn more about bidirectional Unicode characters
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| #include <iostream>
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| using namespace std;
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| const unsigned NUM = 10;
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| typedef unsigned TNumbers[NUM];
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| unsigned checkDivisors(unsigned i);
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| int main() {
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| for (unsigned i = 20; i==i; i += 20) {
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| if (checkDivisors(i)==NUM) {
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| cout << i;
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| return 0;
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| }
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| }
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| return 0;
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| }
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| unsigned checkDivisors(unsigned i) {
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| TNumbers div = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20};
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| unsigned c = 0;
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| for (unsigned j = 0; j < NUM; j++) {
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| if (i%div[j]==0) c++;
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| }
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| return c;
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| }
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What is the smallest number that is divisible by all numbers from 1 to 10?
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
Who Found 2520?
Discovered by the great sage Srinivasa Ramanujan, let's observe the number 2520. Ramanujan outnumbered mathematics, contributed immensely to the number theory, infinity series, continued fractions, and much more. The number 2520 seems to be one of many numbers, but in reality, it is not.
What are numbers divisible by 10 called?
Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10. Example: 10, 20, 30, 1000, 5000, 60000, etc.
What is a number that can only be divided by itself and 1?
A prime number is a number that can only be divided by itself and 1 without remainders. What are the prime numbers from 1 to 100? The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
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