Can someone help me with this question
How many integers from 1 to 10000 inclusive, are multiples of 2 and 5?
A number divisible by two integers a, b which are relatively prime to each other, is divisible by the product of a and b.
So a number divisible by 2 AND 5 is divisible by 2*5=10.
How many integers between 1 and 10 are divisible by 2 AND 5?
Between 1 and 100?
Between 1 and 1000?
Between 1 and 10000?
BTW 1 and 10 = 1
BTW 1 and 100 =10
BTW 1 and 1000= 100
BTW 1 and 10000 = 1000
Am I following this correctly
Good!
Sure! To find the number of integers from 1 to 10000 that are multiples of both 2 and 5, we need to determine the common multiples of these two numbers.
First, we find the multiples of 2 from 1 to 10000. Since every even number is a multiple of 2, we can divide 10000 by 2 to find the number of even integers from 1 to 10000.
10000 ÷ 2 = 5000
So there are 5000 even integers between 1 and 10000.
Next, we find the multiples of 5 from 1 to 10000. To do this, we divide 10000 by 5 to find the number of integers divisible by 5.
10000 ÷ 5 = 2000
Thus, there are 2000 integers divisible by 5 between 1 and 10000.
Since we are looking for numbers that are multiples of both 2 and 5, we need to find the common multiples of these two sets. This can be done by finding the least common multiple (LCM) of 2 and 5, which is 10.
Now, we divide the total number of integers divisible by 10 between 1 and 10000.
10000 ÷ 10 = 1000
Hence, there are 1000 integers that are multiples of both 2 and 5 between 1 and 10000.