Find the least number such that
876xy
is divisible by 20.
y=0 wouldn't work since 876*0 = 0, which doesn't divide by 20
To find the least number such that 876xy is divisible by 20, we need to find the smallest value for xy that results in a number divisible by 20.
A number is divisible by 20 if it is divisible by both 4 and 5.
To be divisible by 4, the last two digits of the number must be divisible by 4. The possible values for xy are 00, 04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, and 96.
To be divisible by 5, the last digit must be either 0 or 5. So the possible values for xy are 00, 20, 40, 60, 80.
To find the smallest value for xy, we start with the smallest value of x which is 0, and then the smallest value of y which is also 0. Therefore, the least number such that 876xy is divisible by 20 is 87600.
To find the least number such that 876xy is divisible by 20, we need to find the smallest possible value for xy that will make the entire number divisible by 20.
To determine if a number is divisible by 20, we need to check if it is divisible by both 4 and 5. A number is divisible by 4 if the last two digits are divisible by 4, and a number is divisible by 5 if the last digit is either 0 or 5.
To simplify the problem, we can start by looking at the last two digits, xy. We need to find the smallest value for xy that is divisible by 4. To do this, we can look at the pattern of numbers that are divisible by 4:
04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96
From this pattern, we see that the smallest value for xy that is divisible by 4 is 04. However, we also need to make sure that the entire number 876xy is divisible by 5.
To check if 876xy is divisible by 5, we only need to look at the last digit, y. Since y can be any number, we want to find the smallest value for y that is divisible by 5. From the pattern of numbers divisible by 5:
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95
From this pattern, the smallest value for y that is divisible by 5 is 0.
So, the least number such that 876xy is divisible by 20 is:
876xy = 87604
Therefore, the answer is 87604.
y=0
876x must be even
So, what do you think?