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If a number divides two different number...

If a number divides two different numbers, then it divides their sum also.

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To determine whether the statement "If a number divides two different numbers, then it divides their sum also" is true or false, we can follow these steps: ### Step 1: Understand the Statement The statement suggests that if a number (let's call it 'd') can divide two different numbers (let's call them 'a' and 'b'), then 'd' should also be able to divide the sum of those two numbers (a + b). ### Step 2: Choose Two Different Numbers Let's select two different numbers. For example, we can choose: - a = 10 - b = 20 ### Step 3: Identify a Common Divisor Now, we need to find a number that divides both 10 and 20. Let's take: - d = 5 ### Step 4: Check if 'd' Divides 'a' and 'b' Now we check: - 10 ÷ 5 = 2 (which is an integer, so 5 divides 10) - 20 ÷ 5 = 4 (which is also an integer, so 5 divides 20) ### Step 5: Calculate the Sum of 'a' and 'b' Next, we calculate the sum of the two numbers: - a + b = 10 + 20 = 30 ### Step 6: Check if 'd' Divides the Sum Now we check if 'd' divides the sum: - 30 ÷ 5 = 6 (which is an integer, so 5 divides 30) ### Conclusion Since we have shown that 'd' (which is 5) divides both 'a' (10) and 'b' (20), and it also divides their sum (30), we can conclude that the statement is true. ### Final Answer The statement "If a number divides two different numbers, then it divides their sum also" is **True**. ---
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