justine a security guard has 3 successive night duties a week when will they see again if they are together now. find gcf
Why didn't you post the complete question?
To find the Greatest Common Factor (GCF) or the highest number that divides evenly into two or more numbers, we need to determine the intervals at which the security guard's duties repeat.
Since Justine has 3 successive night duties every week, we can determine that the pattern repeats every 3 days. To find when they will see each other again, we need to find the least common multiple (LCM) of the two numbers, which is the smallest common multiple of two or more numbers.
In this case, we need to find the LCM of 7 (days in a week) and 3 (the repeating pattern). To find the LCM, we can use the formula:
LCM(a, b) = (a * b) / GCF(a, b)
So, to find the LCM(7, 3):
LCM(7, 3) = (7 * 3) / GCF(7, 3)
Now, let's find the GCF(7, 3):
We can use the Euclidean algorithm to find the GCF:
1. Divide 7 by 3: 7 ÷ 3 = 2 remainder 1
2. Divide 3 by 1: 3 ÷ 1 = 3 remainder 0
Since the remainder is 0, the GCF of 7 and 3 is 1.
Now, let's substitute it back to find the LCM:
LCM(7, 3) = (7 * 3) / 1
= 21
Therefore, Justine and the other person will see each other again in 21 days.