factors theory of nb

Question

If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

kvcpk · Answer

112 = 16 * 7
33 = 11 * 3

a * 43 * 62 * 1311 = (2 ^4 * 7) * k1
a * 43 * 31 * 2 * 1311 = (2^4 *7) * k1
a * 43 * 31 * 2 * 3 *437 = (2^4 *7) * k1

therefore minimum value of a shud be 2^3 * 7 = 56

for the second factor,

a * 43 * 62 * 1311 = (11 * 3) * k2
a * 43 * 31 * 2 * 3 *437 = (11 * 3) * k2

so min = 11

on the whole it shud be 56 * 11 = 616

let me know OA?

amising6 · Answer

If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

a*43*62*1311
a*43*2*31*3*19*23

now we know 33 is a factor this means a should be multiple of 11

now we also know that 112 is a factor
112=2*2*2*2*7
so we can see that a*43*2*31*3*19*23 contains only one 2 and no 7
so a should also contain 2*2*2 and one 7
so a=2*2*2*7*11=616

amising6 · Answer

kvcpk wrote:112 = 4 * 11 * 3
33 = 11 * 3 this is not required.. bcos 112 is factor implies that 33 is factor(how can you say this)

a * 43 * 62 * 1311 = (4 * 11 * 3) * k1
a * 43 * 31 * 2 * 1311 = (4 * 11 * 3) * k1
a * 43 * 31 * 2 * 3 *437 = (4 * 11 * 3) * k1

therefore minimum value of a shud be 2 * 11 = 22

let me know OA?

kvcpk · Answer

amising6 wrote:kvcpk wrote:112 = 4 * 11 * 3 33 = 11 * 3 this is not required.. bcos 112 is factor implies that 33 is factor(how can you say this) a * 43 * 62 * 1311 = (4 * 11 * 3) * k1 a * 43 * 31 * 2 * 1311 = (4 * 11 * 3) * k1 a * 43 * 31 * 2 * 3 *437 = (4 * 11 * 3) * k1 therefore minimum value of a shud be 2 * 11 = 22 let me know OA? Sorry!! My mistake.. messed up 112 with 132... thanks for noting it.. will modify now..

jube · Answer

112 =2^4 * 7 33=11*3 factors which the number already has: 43 62 = 2*31 1311 = 3*19*23 therefore a has to have 2^3*7*11 in it or a=616

francoisph · Answer

sorry it is 11^2 and 3^3

sk818020 · Answer

I also got 616 as the answer for similar reasoning as posted above. Could you please post what the official explanation was if you saying the OA is 11^2 and 3^3 so that we might all learn from this problem?

Thanks,

Jared

francoisph · Answer

If both 11^2 and 3^3 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

11^2 is a factor of the given number.
The number does not have a power or multiple of 11 as its factor.
Hence, "a" should include 11^2
3^3 is a factor of the given number. 6^2 is a part of the number. 6^2 has 3^2 in it.
Therefore, if 3^3 has to be a factor of the given number a * 43 * 62 * 1311, then we will need at least another 3.
Therefore, "a" should be at least 11^2 * 3 = 363 if the given number has to have 11^2 and 3^3 as its factors.
The smallest value that "a" can consequently take is 363.

Could someone explain clearly please?
I didnt get the official explanation

sk818020 · Answer

francoisph wrote:If both 11^2 and 3^3 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

11^2 is a factor of the given number.
The number does not have a power or multiple of 11 as its factor.
Hence, "a" should include 11^2
3^3 is a factor of the given number. 6^2 is a part of the number. 6^2 has 3^2 in it.
Therefore, if 3^3 has to be a factor of the given number a * 43 * 62 * 1311, then we will need at least another 3.
Therefore, "a" should be at least 11^2 * 3 = 363 if the given number has to have 11^2 and 3^3 as its factors.
The smallest value that "a" can consequently take is 363.

Could someone explain clearly please?
I didnt get the official explanation

The prime factorization of a*43*62*1311 = 2*3*19*23*31*43*a

The prime factorization of 112 = 2^4*7

The prime factorization of 33 = 3*11

Because a*43*62*1311 has 2 and 3, the smallest possible number a could be = (2^3)*7*11 = 616

Hope that helps.

Thanks,

Jared

francoisph · Answer

the official explanation A. 121 B. 3267 C. 363 D. 33 E. None of the above The correct choice is (C) and the correct answer is 363.

sk818020 · Answer

francoisph wrote:the official explanation

A. 121
B. 3267
C. 363
D. 33
E. None of the above

The correct choice is (C) and the correct answer is 363.

That is why your throwing everyone off, lol!

You incorrectly put 112 and 33 in your original post when you meant, 11^2 and 3^3.

francoisph · Answer

lol o:) power mate 11^2 and 3^3 are factors of the number a * 43 * 62 * 1311

sk818020 · Answer

francoisph wrote:lol o:) power mate 11^2 and 3^3 are factors of the number a * 43 * 62 * 1311 I also think its supposed to be 6^2. Please confirm.

francoisph · Answer

apologies guys 11 power 2 and 3power 3 are factors of the number a * 4power 3 * 6 power 2 * 13power 11

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