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Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 20:55
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Competition Mode Question What is the unit's digit in the product \(2467^{153} * 341^{72}\)? (A) 0 (B) 1 (C) 2 (D) 7 (E) 9 Find the unit's digit in the product (2467)^153 * (341)^72
(A) 0 (B) 1 (C) 2 (D) 7 (E) 9
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Re: Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 21:34
Unit digit of \(2467^{153}∗341^{72}\) is same as unit digit of \(7^{153}∗1^{72}\) = \(7^{153}\) = \(7^{4*38 + 1}\) (Since cyclicity of 7 is 4) = \(7^1\) = \(7\)
IMO Option D
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Re: Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 21:35
2467^153 x 341^72 Taking each of the terms separately and computing the unit digits correspondingly, we get 341^72 but the unit digit of 341 is 1. all powers of 1 will result in 1, hence the unit digit of 341^72=1 2467^153 the unit digit of 2467 = 7. The unit digits of the powers of 7 are as follows: 7^1=7 7^2=9 7^3=3 7^4=1 7^5=7 7^6=9 so we can see that the cyclicity of the powers of 7 is 4 hence 153/4 =38*4 + 1 Therefore the unit digit lies at the 5th position or 5th power of 7 i.e. unit digit of 7^153 = unit digit of 7^5 = 7
hence unit digit of 2467^153 x 341^72 = 7x1 = 7.
The answer is therefore D.



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Re: Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 21:35
Ans D  7
2467^153∗341^72
Units digit of the product is dependent on the units digits of 2467^153 and 341^72. The units digits of 1^72 would be 1 because 1's cyclicity is 1. Units digit of 2467^153 is 7. The cyclicity of 7 is 4. 7^0 =1 7^1 =1 7^2 = 9 7^3 = 3 7^4 = 1 7^5 = 7
So, the multiplication of these two numbers would be 7*1 = 7



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Re: Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 21:55
153=4K+1
7^4k+1 = last digit is 7 341^72 = last digit is 1 so 7*1 =7
OA:D



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Re: Find the unit's digit in the product 2467^153*341^72
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26 Sep 2019, 23:16
Since unit digit of 341 is 1 which would always result in unit digit of 1, on multiplying with \(2467^{153}\) it would be equal to unit digit of \(7^{153}\). \(2467^{153} * 341^{72} = 2467^{153} * 1^{72}\) \(= 7^{153}\) \(= 7^{38*4 + 1}\) \(= 7^{38*4} * 7^1\) = 1 * 7 = 7 Answer (D).
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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 03:38
cyclicity of 7 ; 7,9,3,1 unit digit of 2467^153 = 7 and 341^72 = 1 so answer IMO D ; 7
What is the unit's digit in the product 2467^153∗341^72?
(A) 0 (B) 1 (C) 2 (D) 7 (E) 9



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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 03:45
Quote: What is the unit's digit in the product \(2467^{153}∗341^{72}\)?
(A) 0 (B) 1 (C) 2 (D) 7 (E) 9 \(units:2467^{153}∗341^{72}=7^{153}*1^{72}=7^{153}\) \(cycles[7]:(7,9,3,1)=4\) \(7^{153}…\frac{153}{4}=remainder[1]=1st.of=(7,9,3,1)=7\) Answer (D)



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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 08:01
7^153* 1^72; 153/4 = 1 remainder (and 0 remainder for 72/4) 7 ^1 * 1 ^4 = 7 * 1 = 7. Ans. D



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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 08:36
Cyclicity of 7 is 4 and that of 1 is 1
Hence, unit digit of 7^153 is 7 and 1^72 is 1
Unit digit of the expression is 7
D is correct



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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 09:05
A number with 7 in unit's digit to the powers has the cycle of numbers 7,9,3,1 respectively. So, the sycle is 4. 153÷4=38+1. So, 2467^153 has 7 in its unit's digit. 7×1=7 Option D Posted from my mobile device
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Re: Find the unit's digit in the product 2467^153*341^72
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27 Sep 2019, 12:14
Units first number 7 >>> Therefore we need to know the cicle of 7 >>> (7,4,1,7,4,1) >>> The cicle repeats each three numbers.
153/3= 51 >> remainder = 0 therefore the units digit of the first number is 1 since the last number of the cicle is 1 (No remainder so last number of the cicle)
Units digit second number is 1, therefore the units digit of this number to any power will be 1.
1*1=1



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Re: Find the unit's digit in the product 2467^153*341^72
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28 Sep 2019, 06:10
What is the unit's digit in the product \(2467^{153}∗341^{72}\)??
\(...7^{153}\)
\(...7^{1}=...7\) \(...7^{2}=...9\) \(...7^{3}=...3\) \(...7^{4}=...1\) .................. \(...7^{5}=...7\) \(...7^{6}=...9\) \(...7^{7}=...3\) \(...7^{8}=...1\) It is repeated in every four terms. So, \(...7^{149}=...7\) \(...7^{150}=...9\) \(...7^{151}=...3\) \(...7^{152}\)=...1 ...\(7^{153}\)=...7
\(341^{72}=...1^{72}\)=...1 Units digit of this number always ends with 1.
Units digit is 7*1=7
The answer is D.
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Re: Find the unit's digit in the product 2467^153*341^72
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29 Sep 2019, 07:48
Solution Given• We are given an expression: 2467^153∗341^72 To find• The units digit of 2467^153∗341^72 Approach and Working out• The units digit of 2467^153∗341^72 is same as the units digit of 7^153∗1^72 Units digits of 7^153∗1^72 = Units digits of 7^153∗ Units digits of 1^72 • = Units digits of 7^153 * 1 Units digits of 7^153 = Units digits of 7^(4*38 +1) = Units digits of 7^1 = 7 Hence, Units digits of 7^153∗1^72 = 7 * 1 = 7 Thus, option D is the correct answer. Correct Answer: Option D
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Re: Find the unit's digit in the product 2467^153*341^72
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