A group has 36 guards. When they march, they form rows of equal numbers of guards. What numbers of rows can they make? How many guards will be in each row?
36
= 1x36
= 2x18
= 3x12
= 4x9
= 6x6
= 9x4
= ....
To find the possible numbers of rows and the number of guards in each row, we need to find the factors of 36.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Now, we can check the numbers of guards in each row by dividing 36 by each factor.
Dividing 36 by 1 gives us 36 guards in each row.
Dividing 36 by 2 gives us 18 guards in each row.
Dividing 36 by 3 gives us 12 guards in each row.
Dividing 36 by 4 gives us 9 guards in each row.
Dividing 36 by 6 gives us 6 guards in each row.
Dividing 36 by 9 gives us 4 guards in each row.
Dividing 36 by 12 gives us 3 guards in each row.
Dividing 36 by 18 gives us 2 guards in each row.
Dividing 36 by 36 gives us 1 guard in each row.
Therefore, the possible numbers of rows are 1, 2, 3, 4, 6, 9, 12, 18, and 36. And the corresponding number of guards in each row are also 1, 2, 3, 4, 6, 9, 12, 18, and 36, respectively.
To find the numbers of rows the group can make and the number of guards in each row, we need to find the factors of 36.
1. List out the factors of 36:
Divisor: 1 2 3 4 6 9 12 18 36
Factors: 36 18 12 9 6 4 3 2 1
2. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Now we can determine the numbers of rows and the number of guards in each row based on these factors.
Possible numbers of rows:
The number of rows for each factor is the total number of guards divided by the factor.
For example:
If we divide 36 guards into rows of 1, we would have 36 rows with 1 guard in each row.
If we divide 36 guards into rows of 2, we would have 18 rows with 2 guards in each row.
If we divide 36 guards into rows of 3, we would have 12 rows with 3 guards in each row.
And so on...
Therefore, the numbers of rows the group can make are:
1 row, 2 rows, 3 rows, 4 rows, 6 rows, 9 rows, 12 rows, 18 rows, and 36 rows.
Number of guards in each row:
The number of guards in each row is equal to the factor we used to divide the total number of guards.
For example:
If we divide 36 guards into rows of 1, there would be 1 guard in each row.
If we divide 36 guards into rows of 2, there would be 2 guards in each row.
If we divide 36 guards into rows of 3, there would be 3 guards in each row.
And so on...
Therefore, the number of guards in each row would be:
1 guard, 2 guards, 3 guards, 4 guards, 6 guards, 9 guards, 12 guards, 18 guards, and 36 guards.