# Find the number of integers

• Nov 30th 2009, 01:32 AM
yshridhar
Find the number of integers
Find the number of integers from 1 to 10,000 which are divisible by either 13 or 51
regards
Sridhar
• Nov 30th 2009, 05:38 AM
Hello yshridhar

Welcome to Math Help Forum!
Quote:

Originally Posted by yshridhar
Find the number of integers from 1 to 10,000 which are divisible by either 13 or 51
regards
Sridhar

$\displaystyle 10,000\div13 = 769.1$, so there are $\displaystyle 769$ integers from $\displaystyle 1$ to $\displaystyle 10,000$ that are divisible by $\displaystyle 13$.

In the same way, you can find the number of integers that are divisible by $\displaystyle 51$.

Add this number to $\displaystyle 769$. Then you will need to subtract the number of integers that are divisible by $\displaystyle 13\times51\; (= 663)$, because they will have been counted twice. (Note that $\displaystyle 51 = 3 \times 17$, so $\displaystyle 51$ and $\displaystyle 13$ have no common factors.)

Can you complete this now?