Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

What is the last digit of this number? 22223333

Answer
VerifiedVerified
442.2k+ views
like imagedislike image
Hint: To obtain the last digit of the number given we will use the recognizing pattern of number method. Firstly we will see what the last digit of starting power of 2 is. Then we will see how the pattern works and then accordingly we will solve the given number without actually multiplying it and get our desired answer.

Complete step by step solution:
The number is given as:
22223333
As we know that power of 2 have following values:
21=222=423=824=16
25=3226=6427=12828=256
As we can see, the last digit of the first four terms is 2,4,8,6 and then after that the last digit of next four terms is 2,4,6,8.
So we can conclude that the power of any number where the last digit is 2 will have the same pattern.
After a group of 4 the pattern starts again.
So as the power of the number 2222 is 3333 we have to find where 3333 falls in the above pattern.
The pattern repeats after 4 values so we will divide 3333 by 4 as below:
3333÷433334
83314
So by above value we get the pattern continues for 833 times and then one more time.
So we get that
22223332 Last digit will be 6
22223333 Last digit will be 2

Hence last digit of 22223333 is 2

Note:
There are numbers of tools that are used to solve such types of problems such as modular arithmetic, Chinese remainder theorem and also Euler’s theorem but the recognizing the pattern is much simpler and easy to remember. Every number has a different pattern when we raise their power we just have to be observant in order to get the answer.
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for MAHARASHTRABOARD students
PhysicsPhysics
BiologyBiology
ChemistryChemistry
MathsMaths
₹36,600 (9% Off)
₹33,300 per year
Select and buy