What is the units digit of 3^67?
A. 1
B. 3
C. 5
D. 7
E. 9
*An answer will be posted in 2 days.
What is the units digit of 367?
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The unit digits of 3base powers follow this sequence: 3, 9, 7, 1
Indeed:
3^1 = 3 => unit digit is 3
3^2 = 9 => unit digit is 9
3^3 = 27 => unit digit is 7
3^4 = 81 => unit digit is 1
3^5 = 243 => unit digit is 3
If 3 is raised to 67th power, the unit digit numbers will repeat this sequence until it stops at 67th power. Because the remainder of the division of 67 by 4 is 3 (16*4 + 3 =67), the digit number of the 67th power will be the third number in the sequence.
So the answer is 7
Indeed:
3^1 = 3 => unit digit is 3
3^2 = 9 => unit digit is 9
3^3 = 27 => unit digit is 7
3^4 = 81 => unit digit is 1
3^5 = 243 => unit digit is 3
If 3 is raised to 67th power, the unit digit numbers will repeat this sequence until it stops at 67th power. Because the remainder of the division of 67 by 4 is 3 (16*4 + 3 =67), the digit number of the 67th power will be the third number in the sequence.
So the answer is 7
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We get (~3)^1=~3, (~3)^2=~9, (~3)^3=~7, (~3)^4=~1. Units digit repeats 3ïƒ 9ïƒ 7ïƒ 1ïƒ 3. Then, 3^67=3^[4(16)+3]ïƒ 3^3=~7. Hence, the units digit becomes 7, and the correct answer is D.
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Think of it like this  the pattern for the unit's digit for base 3 goes as follows:jain2016 wrote:Hi Experts,
Can you please explain the below part?
3 (16*4 + 3 =67)
Thanks,
SJ
3^1 > 3
3^2 > 9
3^3 > 7
3^4 > 1
3^5 > 3
3^6 > 9
3^7 > 7
3^8 > 1
So the pattern repeats every four terms. Put another way, every time the exponent is a multiple of 4, the units digit is '1.' Now we can think of a multiple of 4 that's close to 67. (So think either 64, as the above example does, or 68. Let's use 68.)
3^65 > 3
3^66 > 9
3^67 > 7
3^68 > 1

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This explanation is very good and easy to follow that i also got D as the answer
The unit digits of 3base powers follow this sequence: 3, 9, 7, 1
Indeed:
3^1 = 3 => unit digit is 3
3^2 = 9 => unit digit is 9
3^3 = 27 => unit digit is 7
3^4 = 81 => unit digit is 1
3^5 = 243 => unit digit is 3
If 3 is raised to 67th power, the unit digit numbers will repeat this sequence until it stops at 67th power. Because the remainder of the division of 67 by 4 is 3 (16*4 + 3 =67), the digit number of the 67th power will be the third number in the sequence.
So the answer is 7
The unit digits of 3base powers follow this sequence: 3, 9, 7, 1
Indeed:
3^1 = 3 => unit digit is 3
3^2 = 9 => unit digit is 9
3^3 = 27 => unit digit is 7
3^4 = 81 => unit digit is 1
3^5 = 243 => unit digit is 3
If 3 is raised to 67th power, the unit digit numbers will repeat this sequence until it stops at 67th power. Because the remainder of the division of 67 by 4 is 3 (16*4 + 3 =67), the digit number of the 67th power will be the third number in the sequence.
So the answer is 7
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The pattern of units digits of the base of 3 is 3971. Thus, 3^68 has a units digit of 1, so 3^67 has a units digit of 7.[email protected] Revolution wrote: ↑Sat May 21, 2016 4:40 pmWhat is the units digit of 3^67?
A. 1
B. 3
C. 5
D. 7
E. 9
*An answer will be posted in 2 days.
Answer: D
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