Flag Algebra> If N = 7^2014 Then: A) The Last Digit is ...
question mark

If N = 7^2014 Then:
A) The Last Digit is 7
B) Remainder upon division by 24 is 1
C) Remainder upon division by 25 is 1
D) No. Of digits in N > 1700

Shadic The Hedgehog , 5 Years ago
Grade 11
anser 1 Answers
Aditya Gupta

Last Activity: 5 Years ago

N= 7^(2*1007)= (7^2)^(1007)= 49^1007
= (48+1)^1007
= 48k + 1 (using binomial theorem, k is an integer).
= 24(2k)+1
= 24q + 1
hence, the remainder is 1 when divided by 24.
for remainder by 25, write 49= 50 – 1= 25(2) – 1,and you ll find N= 25q – 1= 25(q – 1) + 24, hence remainder is 24 not 1.
for last digit, we simply need to find remainder on division by 10, write 49= 50 – 1= 10*5 – 1 and then proceed.
KINDLY APPROVE :))

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments