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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? Updated on: 10 May 2020, 10:55
Originally posted by GMATBusters on 09 May 2020, 18:53.
Last edited by GMATBusters on 10 May 2020, 10:55, edited 3 times in total.
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E
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GMATBusters’ Quant Quiz Question -3

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If m = 7^20 + 7^21 + 7^22, what is the largest prime factor of m?

A. 3
B. 7
C. 13
D. 17
E. 19
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E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 18:55
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Official Solution:



m = 7^20 + 7^21 + 7^22
= 7^20( 1+7+49)
= 7^20(57)
= 3*19*7^20

the largest prime factor = 19.

Hence Answer is E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:05
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m?
m = 7^20 (1+7^1+7^2)
m= 7^20 (1+7+49)
m = 7^20 (57)
m = 7^20 (19*3)

A. 3
B. 7
C. 13
D. 17
E. 19

Ans. E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:09
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m = 7^20 +7^21 +7^22
m = 7^20(1+7+49)
m= 7^20 * 57
m=7^20.19.3

So the largest prime factor = 19
Ans - E

Hence,
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:13
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Answer E. As 7(57) and 19*3 = 57

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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:16
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m=19*3*7^20
Largest prime facor=19
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:33
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m can be re written as
m = 7^20*(1+7^1+7^2)
m= 7^20*57
m=7^20*3*19
largest prime factor is 19
OPTION E

If m = 7^20 +7^21 +7^22, what is the largest prime factor of m?
A. 3
B. 7
C. 13
D. 17
E. 19
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 19:36
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m= 7^20 +7^21 +7^22.
We need to divide m into its prime factors.
m= 7^20 ( 1+7^1+7^2)
m= 7^20 (1+7+49)
m= 7^20 * 57
m= 7^20 * 3* 19
Thus, m has 3 prime factors of which 19 is the largest prime factor.
Answer: E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? Updated on: 10 May 2020, 08:18
Originally posted by Kinshook on 09 May 2020, 20:32.
Last edited by Kinshook on 10 May 2020, 08:18, edited 1 time in total.
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Asked: If m = 7^20 +7^21 +7^22, what is the largest prime factor of m?

A. 3
B. 7
C. 13
D. 17
E. 19

m = 7^20 +7^21 +7^22 = 7^20(7^2 + 7 + 1) = 7^20(49+ 7+ 1) = 7^20*57 = 7^20*3*19

Largest prime factor of m = 19

IMO E

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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 20:46
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m = 7^20 + 7^21 + 7^22 = 7^20(1 + 7 + 49) = 7^20 x 57 = 7^20 x 3 x 19
Prime factors are 3, 7, 19
Largest prime factor = 19

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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 09 May 2020, 21:51
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The answer is E which is 19.
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 10 May 2020, 00:10
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let's say 7^20 = A
m can be expressed as m = A + 7A + 49A = 57A = 3 x 19 x A
Hence, 3, 19 and 7 are factors of m and 19 is the largest prime factor. E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 10 May 2020, 00:54
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Quote:
If m = 7^20 +7^21 +7^22, what is the largest prime factor of m?
A. 3
B. 7
C. 13
D. 17
E. 19
Show more

= \(7^{20}( 1 + 7 + 7^2)\)

= \(7^{20}( 1 + 7 + 49)\)

= \(7^{20}(57)\)

= \(7^{20}(19*3)\) , Highest prime factor is 19 , Answer must be (E)
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 10 May 2020, 02:25
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m = 7^20 + 7^21 + 7^22
= 7^20 * (1+7+49)
= 7^20 * 57
= 7^20 * 3* 19

Thus, the largest prime factor of m is 19

FINAL ANSWER IS (E)

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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 10 May 2020, 03:36
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If m = 7^20 + 7^21 + 7^22, what is the largest prime factor of m?

A. 3
B. 7
C. 13
D. 17
E. 19

m = 7^20(1+7+49) = 7^20* 57 = 7^20*3*19

Largest prime factor = 19 - Answer - E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 10 May 2020, 04:38
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m=7^20 + 7^21 + 7^22
= 7^20 (1 + 7 + 49)
= 7^20*57
=7^20*19*3
= highest prime factor is hence 19.
OA E
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If m = 7^20 +7^21 +7^22, what is the largest prime factor of m? 08 Apr 2025, 09:09
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