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The sum of two numbers 10373 + 24871 is divisible by:
- a)7
- b)8
- c)6
- d)13
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of two numbers 10373 + 24871 is divisible by:a)7b)8c)6d)13Corr...
Concept used:
Divisibility law of 6 ⇒ A number is divisible by 6 if the sum of its digit is divisible by 3 and the last digit is even.
Divisibility law of 7
: Take the last digit of the number, double it Then subtract the result from the rest of the number If the resulting number is evenly divisible by 7If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
The divisibility rule of 13 states that: Add the unit place digit after multiplication with 4 to the remaining number to the left of the digit at units place. If the result of the addition is divisible by 13, then the complete number is also divisible by 13.
Calculation
⇒ 10373 + 24871 = 35244
Option 1:
⇒ 35244 - 4
×
2 = 35236 ⇒ 35236 - 4
×
6 = 35212
35212 is not divisible by 7, so 35244 is also not divisible by 7.
Option 2:
last three digits of the number i.e. 244 is not divisible by 8, hence
35244 is also
not divisible by 8.
Option 3
:
⇒ 3 + 5 + 2 + 4 + 4 = 18
The sum of its digit is divisible by 3 and the last digit is even, hence number is divisible by 6.
Option 4
:
⇒ 35244 + 4
×
4 = 3540
3540 is not divisible by 13, so 3540 is also not divisible by 13.
The answer is option 3.
Most Upvoted Answer
The sum of two numbers 10373 + 24871 is divisible by:a)7b)8c)6d)13Corr...
Understanding Divisibility
To determine whether the sum of two numbers, 10373 + 24871, is divisible by 6, we must check two conditions: divisibility by 2 and divisibility by 3.
Step 1: Calculate the Sum
- First, calculate the sum:
- 10373 + 24871 = 35244
Step 2: Check Divisibility by 2
- A number is divisible by 2 if its last digit is even.
- The last digit of 35244 is 4, which is even.
- Therefore, 35244 is divisible by 2.
Step 3: Check Divisibility by 3
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Sum of the digits in 35244:
- 3 + 5 + 2 + 4 + 4 = 18
- Now, check if 18 is divisible by 3:
- 18 ÷ 3 = 6 (which is an integer)
- Therefore, 35244 is also divisible by 3.
Conclusion
- Since 35244 is divisible by both 2 and 3, it is divisible by 6.
- Thus, the correct answer is option 'C', confirming that the sum is indeed divisible by 6.
This analysis shows that the sum of the two numbers meets the criteria for divisibility by 6, thereby justifying the conclusion.
To determine whether the sum of two numbers, 10373 + 24871, is divisible by 6, we must check two conditions: divisibility by 2 and divisibility by 3.
Step 1: Calculate the Sum
- First, calculate the sum:
- 10373 + 24871 = 35244
Step 2: Check Divisibility by 2
- A number is divisible by 2 if its last digit is even.
- The last digit of 35244 is 4, which is even.
- Therefore, 35244 is divisible by 2.
Step 3: Check Divisibility by 3
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Sum of the digits in 35244:
- 3 + 5 + 2 + 4 + 4 = 18
- Now, check if 18 is divisible by 3:
- 18 ÷ 3 = 6 (which is an integer)
- Therefore, 35244 is also divisible by 3.
Conclusion
- Since 35244 is divisible by both 2 and 3, it is divisible by 6.
- Thus, the correct answer is option 'C', confirming that the sum is indeed divisible by 6.
This analysis shows that the sum of the two numbers meets the criteria for divisibility by 6, thereby justifying the conclusion.
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The sum of two numbers 10373 + 24871 is divisible by:a)7b)8c)6d)13Correct answer is option 'C'. Can you explain this answer?
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