# Abc is a three digit numer where a,b,c are the digits. How many are there such that a*b*c=12

2
by nikki23

Log in to add a comment

by nikki23

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Factors of 12 are : 1 , 2, 3, 4, 6 which are single digits.

so a, b, c are from 1,2,3,4,6.

Combinations/groups of digits which result in 12 :

1 , 2 , 6, ;; 2, 2, 3 ;; 1 , 3, 4 ;;;

For the 1st and third groups of these 3 digit groups, there are 3! or 3P3 permutations possible. So there are 6 numbers in each group. Hence, there are 12 such numbers.

In the second group, as two digits are same, the permutations are 3! /2 = 3 only.

*hence there are totally 15 such numbers.*

these are :

126, 162, 216,261,612,621,;;

223,232;;322 ;;;;

134, 143, 314, 341, 413, 431

so a, b, c are from 1,2,3,4,6.

Combinations/groups of digits which result in 12 :

1 , 2 , 6, ;; 2, 2, 3 ;; 1 , 3, 4 ;;;

For the 1st and third groups of these 3 digit groups, there are 3! or 3P3 permutations possible. So there are 6 numbers in each group. Hence, there are 12 such numbers.

In the second group, as two digits are same, the permutations are 3! /2 = 3 only.

these are :

126, 162, 216,261,612,621,;;

223,232;;322 ;;;;

134, 143, 314, 341, 413, 431