SOLVE: Determine the smallest counting number having 36 factors, with 6 consecutive factors Please provide the applicable - Maths - Integers

Question

SOLVE:
Determine the smallest counting number having 36 factors, with 6
consecutive factors

​Please provide the applicable and reasonable
solution in steps
{Please don't provide any weblink or certified answer I want only
experts answer}

Brijendra Pal · Accepted Answer

Hi, We know that number of factors are calculated as for example for 24 = 23×31so number of factors = 3+11+1= 8 powers +1 of both factors are multiplied and one more thing factors here will be prime  meaning base of power will be 2,3,5,7,
so if you are taking about 6 consective factors so you are taking about 2,3,5,7,11,13So Number will be like = 2a×3b×5c×7d×11e×13fNow also it is given that a+1b+1c+1d+1e+1f+1= 36 = 2×2×3×3but here minimum value of a,b,c,d,e,f can be 1 to have 6 consective factorsso your question is incorrect as when 6 consecutive factors are taken then number of factors will betaking a=b=c=d=e=f=1 2×2×2×2×2×2= 64 so here it will be 64 factors and not 36

SOLVE: Determine the smallest counting number having 36 factors, with 6 consecutive factors. ​Please provide the applicable and reasonable solution in steps. {Please don't provide any weblink or certified answer... I want only experts answer}

SOLVE:
Determine the smallest counting number having 36 factors, with 6 consecutive factors.

Please provide the applicable and reasonable solution in steps.
{Please don't provide any weblink or certified answer... I want only experts answer}