How many factors of 294 are NOT factors of 112? (A)2 (B)

Question

How many factors of 294 are NOT factors of 112?

(A)2 (B) 4 (C) 6 (D) 8 (E) None of these

jd04 · Answer

I got 6

Prime Factor Tree:

294 = 2*147
147 = 3*49
49 = 7*7
So,
294 = 2*3*7*7
Factors = 1,2,3,6,7,14,21,49,147,294

112 = 2*56
56=7*8
8=2*4
4=2*2
112 = 2*2*2*2*7
Factors = 1,2,4,7,8,14,16,28,56,112

Factors of 294 that are not factors of 112:
3,6,21,49,147,294

Professor · Answer

294 = 2x3x7x7. so its factors are   1  ,   2  , 3, 6,   7  ,   14  , 21, 42, 49, 98, 147, and 294
112 = 2x2x2x2x7. so its factors are   1  ,   2  , 4,   7  , 8,   14  , 16, 28, 56, and 112.

it is 8 (3, 6, 21, 42, 49, 98, 147, and 294).

ps_dahiya · Answer

Simpler method:

294 = 2*3*7^2: Total factors = 2*2*3 = 12
112 = 2^4 * 7: Total factors = 5*2 = 10

Factos that are NOT common = 12-10=   2  

Common terms in both = 2*7
So ,out of 10 factors of 112 common factors are = 2*2 = 4
So ,out of 10 factors of 112 NOT common factors are = 10-4 =   6  

Total factors that are NOT common = 2+6 = 8

mattflow · Answer

112 = 2^4*7, not 2^3

So total factors for 112 = 5*2 = 10.

How many factors of 294 are NOT factors of 112? (A)2 (B)

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards