Question

HELP PLEASE AS SOON AS POSSIBLE
Sarah writes down all 3-digit positive integers for which the product of their digits equals 36. What is the difference between the greatest and the smallest of these 3-digit numbers?

Answer 1

let the no. be 100x+10y+z

xyz =36

these are the possibilities

2×3×6

2×2×9

3×3×4

max. 3 digit among these is 922

min 3 digit 229

difference = 922-229 = 693

Answer 2

Difference between the greatest and the smallest of these 3-digit numbers is 792 for which the product of their digits equals 36.

Given:

All 3-digit positive integers for which the product of their digits equals 36.

To Find:

The difference between the greatest and the smallest of these 3-digit numbers

Solution:

Factors of 36 are  1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36

Hence Digits can be  1 , 2 , 3 , 4 , 6 , 9

3 Digit  positive integers for which the product of their digits equals 36.

Starting with 1

149 , 166 , 194

Starting with 2

229 , 236 , 263 , 294

Starting with 3

326 , 334 , 343 , 362

Starting with 4

419 , 433 , 491

Starting with 6

616 , 623 , 632 , 661

Starting with 9

914 , 922 , 941

Hence 149 is smallest  and  941 is largest

Difference = 941 - 149

= 792

Difference between the greatest and the smallest of these 3-digit numbers is 792