Certainly! Let's work through the problem step by step.
### Part g:
Find the greatest number that divides 582 and 680.
To find the greatest number that divides two numbers, we need to determine their Greatest Common Divisor (GCD).
- Numbers to consider: 582 and 680
First, list the GCD of the numbers.
- The greatest number that divides both 582 and 680 is 2.
### Part h:
Find the greatest number that divides 151, 235, and 295 leaving a remainder of 7 in each case.
To solve this, subtract 7 from each of the numbers and then find the GCD.
- Numbers after subtracting the remainder (7): 151 - 7, 235 - 7, and 295 - 7
- This simplifies to: 144, 228, and 288
Next, find the greatest number that divides 144, 228, and 288 (the GCD).
- The greatest number that divides 144, 228, and 288 leaving a remainder of 7 is 12.
### Part i:
The length and breadth of a carpet are 784 cm and 588 cm respectively. Find the length that measures the two dimensions of the carpet exactly.
To find the length that measures the two dimensions exactly, we need to determine the GCD of the length and breadth.
- Dimensions: 784 cm and 588 cm
Finding the greatest common length:
- The greatest number that exactly measures both 784 and 588 is 196 cm.
### Summary:
- The greatest number that divides 582 and 680 is 2.
- The greatest number that divides 151, 235, and 295 leaving a remainder of 7 is 12.
- The length that measures both dimensions of the carpet (784 cm and 588 cm) exactly is 196 cm.
I hope this explanation helps clarify how to find these greatest numbers!
