A number is multiplied by 46 and 54 respectively. The sum of the two products is 37400. This number is ()

A number is multiplied by 46 and 54 respectively. The sum of the two products is 37400. This number is ()

37400/(46+54)=37400/100=374
So the number is 374

Divide the nine numbers 39, 45, 49, 56, 60, 70, 78, 84 and 91 into three groups so that the products of the three numbers in each group are equal. How can we divide them?
Help qsmm: I have seen your wonderful answer
But I would like to ask, why is [39 × 70 × 84 = 78 × 49 × 60 = 45 × 56 × 91]?
Why decompose the prime factor?
What are the rules?
Looking forward to your reply!
Also welcome other netizens to answer!

The purpose of decomposing the quality factor is to adjust the multiple, because the quality factor can't be divided (that is, it can't be obtained by a × b). If the quality factor is very large, it can be used as the basis
If 70, 60 and 45 are multiples of 5, they must be divided into different groups
39, 78 and 91 are multiples of 13
The remaining 84, 49 and 56 are multiples of 7

39, 45, 49, 56, 60, 70, 78, 84 and 91 are the products of a group. What are the numbers of these groups?

Divide the nine numbers 39.45.49.56.60.70.78.84.91 into three groups to make the product of each group equal

39×45×49×56×60×70×78×84×91
=12059402741568000
The cube root is 229320. Divide 229320 by 45 60 70
The result is 39 × 70 × 84 = 229320
45×56×91=229320
49×60×78=229320