Aptitude Discussion

Q. |
If $N=2^3×3^4$ , $M= 2^2×3×5$, then find the number of factors of $N$ that are common with the factors of $M$. |

✖ A. |
8 |

✔ B. |
6 |

✖ C. |
18 |

✖ D. |
20 |

**Solution:**

Option(**B**) is correct

The factors that are common must also be the factors of $HCF(N,M)$

$HCF(N,M) = 2^2×3$

Number of factors of $2^2×3 = (2+1)(1+1) = 6$

So there are **6** factors that are common to both.

**Shashiii Ghanekar**

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**Saikiran**

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Taking the common values 2^2*3, we get 12.. factors of 12 are 1,2,3,4,6,12.. 6 factors common to M & N.. Is it right too??.. I have a doubt

**Abhay**

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The answer, I reckon, should be 6. The calculation of HCF is wrong.

**Shreya**

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is there some problem in the soln as while taking out the hcf we take the less powers of common prime factors

N=2^3×3^4=648

M= 2^2×3×5=60

N=648/6=108

M=60/6=10

Therefore 6 is the common factor of 648 and 60 i.e. N and M