Cyclicity: Number Theory

# Cyclicity: Number Theory Video Lecture | General Aptitude for GATE - Mechanical Engineering

## General Aptitude for GATE

201 videos|166 docs|152 tests

## FAQs on Cyclicity: Number Theory Video Lecture - General Aptitude for GATE - Mechanical Engineering

 1. What is cyclicity in number theory?
Ans. Cyclicity in number theory refers to the concept of the repeating pattern of the last digit of a number raised to different powers. It helps to determine the period or cycle of the last digit when a number is raised to increasing powers.
 2. How can cyclicity be used to find the last digit of a large power?
Ans. To find the last digit of a large power using cyclicity, we need to determine the cycle of the last digit for the given number. Once the cycle is known, we can divide the power by the cycle length and use the remainder to find the corresponding digit in the cycle.
 3. What is the cycle length of the last digit of powers of 2?
Ans. The cycle length of the last digit of powers of 2 is 4. This means that the last digit of any power of 2 repeats after every fourth power. For example, 2^1 = 2, 2^2 = 4, 2^3 = 8, and 2^4 = 16, where the last digit repeats after 2^4.
 4. Can cyclicity be applied to numbers other than powers of 2?
Ans. Yes, cyclicity can be applied to numbers other than powers of 2. Different numbers have different cyclicity patterns for their last digits. For example, the last digit of powers of 3 has a cycle length of 4 (3, 9, 7, 1), while the last digit of powers of 7 has a cycle length of 4 (7, 9, 3, 1).
 5. How can cyclicity be used to solve problems involving remainders?
Ans. Cyclicity can be used to solve problems involving remainders by considering the cycle length of the last digit. If we need to find the remainder when a number is divided by another number, we can use cyclicity to determine the pattern of the remainders. By dividing the power by the cycle length and considering the remainder, we can find the corresponding remainder in the cyclicity pattern.

## General Aptitude for GATE

201 videos|166 docs|152 tests

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