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Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25?
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Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25?
Dividing the Sum of Exponents by 25
To find the remainder when the sum of \(3^{14} + 4^{14}\) is divided by 25, we need to break down the problem step by step.
Step 1: Calculate the Individual Exponents
- \(3^{14} = 4782969\)
- \(4^{14} = 268435456\)
Step 2: Find the Sum of the Exponents
\(4782969 + 268435456 = 273218425\)
Step 3: Divide the Sum by 25
- \(273218425 \div 25 = 10928737\) with a remainder
Step 4: Finding the Remainder
To find the remainder, we can simplify the problem by looking at the last two digits of the sum.
- \(273218425 \equiv 25 \times 10928737 \equiv 25 \times 37 \equiv 925 \pmod{100}\)
Step 5: Finding the Final Remainder
Since we are interested in finding the remainder when divided by 25, we need to further simplify the problem.
- \(925 \equiv 0 \pmod{25}\)
Therefore, the remainder when the sum of \(3^{14} + 4^{14}\) is divided by 25 is 0.
To find the remainder when the sum of \(3^{14} + 4^{14}\) is divided by 25, we need to break down the problem step by step.
Step 1: Calculate the Individual Exponents
- \(3^{14} = 4782969\)
- \(4^{14} = 268435456\)
Step 2: Find the Sum of the Exponents
\(4782969 + 268435456 = 273218425\)
Step 3: Divide the Sum by 25
- \(273218425 \div 25 = 10928737\) with a remainder
Step 4: Finding the Remainder
To find the remainder, we can simplify the problem by looking at the last two digits of the sum.
- \(273218425 \equiv 25 \times 10928737 \equiv 25 \times 37 \equiv 925 \pmod{100}\)
Step 5: Finding the Final Remainder
Since we are interested in finding the remainder when divided by 25, we need to further simplify the problem.
- \(925 \equiv 0 \pmod{25}\)
Therefore, the remainder when the sum of \(3^{14} + 4^{14}\) is divided by 25 is 0.
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Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25?
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Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25?.
Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the remainder when the sum (3¹⁴+4¹⁴) is divided by 25?.
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