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22 Apr 2010, 07:16
Kudos
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Hi everybody!
I got a question concerning the pattern of getting the units digit in questions like the following:
What is the units digit of 3^17 × 17^54 × 135^19 × 31^21 × 42^17?
Is it true that the units digit is repeated with every 4th power, i.e. 3^2 has the same units digit as 3^6 and 3^10?
My approach:
3^17 ---> 17 divided by 4, remainder 1---> 3^1 ---> Units digit 3
17^54 ---> 54 divided by 4, remainder 2---> 7^2 ---> Units digit 9
135^19 ---> 19 divided by 4, remainder 3---> 5^3 ---> Units digit 5
31^21 ---> 21 divided by 4, remainder 1---> 1^1 ---> Units digit 1
42^17 ---> 17 divided by 4, remainder 1---> 2^1 ---> Units digit 2
3 x 9 x 5 x 1 x 2 = 270
Answer: Units digit = 0.
Would this be a good approach?
I got a question concerning the pattern of getting the units digit in questions like the following:
What is the units digit of 3^17 × 17^54 × 135^19 × 31^21 × 42^17?
Is it true that the units digit is repeated with every 4th power, i.e. 3^2 has the same units digit as 3^6 and 3^10?
My approach:
3^17 ---> 17 divided by 4, remainder 1---> 3^1 ---> Units digit 3
17^54 ---> 54 divided by 4, remainder 2---> 7^2 ---> Units digit 9
135^19 ---> 19 divided by 4, remainder 3---> 5^3 ---> Units digit 5
31^21 ---> 21 divided by 4, remainder 1---> 1^1 ---> Units digit 1
42^17 ---> 17 divided by 4, remainder 1---> 2^1 ---> Units digit 2
3 x 9 x 5 x 1 x 2 = 270
Answer: Units digit = 0.
Would this be a good approach?
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Hussain15
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22 Apr 2010, 07:24
Kudos
Bookmarks
I think you are missing one point here.
The pattern of 4 is not for every number.
Check this link out for cyclicity.
https://takshzilabeta.com/index.php?opti ... -&Itemid=5
In order to solve this very problem, I think you should go through the following thread.
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
Kindly do share the answer of this question too.
The pattern of 4 is not for every number.
Check this link out for cyclicity.
https://takshzilabeta.com/index.php?opti ... -&Itemid=5
In order to solve this very problem, I think you should go through the following thread.
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
Kindly do share the answer of this question too.
22 Apr 2010, 07:40
Kudos
Bookmarks
Your approach is good.
1,1,1,1,1
2,4,8,6,2
3,9,7,1,3
4,6,4,6,4
5,5,5,5,5
6,6,6,6,6
7,9,3,1,7
8,4,2,6,8
9,1,9,1,9
0,0,0,0,0
You can also use that:
1,5,6,0 is repeated with every 1st power (You can ignore power)
4,9 is repeated with every 2nd power (odd|even power = 1st|2nd power)
1,1,1,1,1
2,4,8,6,2
3,9,7,1,3
4,6,4,6,4
5,5,5,5,5
6,6,6,6,6
7,9,3,1,7
8,4,2,6,8
9,1,9,1,9
0,0,0,0,0
You can also use that:
1,5,6,0 is repeated with every 1st power (You can ignore power)
4,9 is repeated with every 2nd power (odd|even power = 1st|2nd power)
