what is the greatest mass that can be taken an exact number of times from 720kg,1008kg and 672kg?
720 1008 672
2 360 504 336
2 180 252 168
2 90 126 84
2 45 63 42
3 15 21 14
2*2*2*2*3=2^4*3 =48kg
I misread 1008 as 1080.
Go with Reiny.
2*2*2*2*3
48
24
To find the greatest mass that can be taken an exact number of times from 720kg, 1008kg, and 672kg, we need to determine the greatest common divisor (GCD) of these three numbers.
Here's how you can find the GCD using the Euclidean algorithm:
1. Start by comparing the first two numbers, 720kg and 1008kg. To do this, divide the larger number (1008kg) by the smaller number (720kg), and find the remainder: 1008kg ÷ 720kg = 1 remainder 288kg.
2. Now, we compare the remainder (288kg) obtained from step 1 with the next number, 672kg. Divide the remainder by 672kg and find the new remainder: 288kg ÷ 672kg = 0 remainder 288kg.
3. Repeat step 2 by comparing the new remainder (288kg) with the number obtained from step 1 (672kg): 672kg ÷ 288kg = 2 remainder 96kg.
4. Continue this process until you reach a remainder of 0. Now compare the last non-zero remainder (96kg) with the previous remainder (288kg): 288kg ÷ 96kg = 3 remainder 0.
5. Since the remainder has become 0, the previous non-zero remainder (96kg) is the GCD of 720kg, 1008kg, and 672kg.
Therefore, the greatest mass that can be taken an exact number of times from 720kg, 1008kg, and 672kg is 96kg.
let me rephrase the question ...
what is the greatest common factor of
720, 1008, and 672 ?
720 = 8*9*10 = 16*3*3*5
1008 = 8*9*14 = 16*3*3*7
672 = 16*3*2*7
so who is common?
looks like 16*3 or 48
check:
720/48 = 15
1008/48 = 21
672/48 = 14 , nothing common in any of those 3 answers.
720 = 2^4 * 3^2 * 5
1080 = 2^3 * 3^3 * 5
672 = 2^5 * 3 * 7
So, the largest number that evenly divides all of those is
2^3 * 3 = 24