Last three digits in 19^100 is A. 001 B. 010 C. 100 D. 999
Added by Michael M.
Step 1
We can do this by calculating the remainder when dividing by 1000 (since we are interested in the last three digits). $19^1 \equiv 19 \pmod{1000}$ $19^2 \equiv 361 \pmod{1000}$ $19^3 \equiv 6859 \equiv 859 \pmod{1000}$ $19^4 \equiv 16321 \equiv 321 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Breanna Ollech and 73 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The last digit of (a) $3^{100}$ is 1 (b) $17^{50}$ is (c) $17^{50}+7^{50}$ is 8 (d) $19^{60}+7^{40}$ is 0
The number $101^{100}-1$ is divisible by (a) 100 (b) 1000 (c) 10000 (d) 100000 .
The last two digits of the number $3^{400}$ are (A) 38 (B) 27 (C) 01 (D) none of these
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD