SOLUTION: The number 632 is a multiple number since the first digit 6 is the product of the other two digits of the number. How many three-digit multiple numbers less than 700 exist?

Algebra.Com
Question 389861: The number 632 is a multiple number since the first digit 6 is the product of the other two digits of the number. How many three-digit multiple numbers less than 700 exist?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
1.  If the first digit is 1, there is only one way to factor 1 using two
    integers, 1×1 = 1, so the only multiple number with 1st digit 1 is 111. 

2.  If the first digit is 2, there are two ways to factor 2 using two
    integers, 1×2 = 2, and 2×1 = 2  so there are two multiple numbers with 1st
    digit 2, 212 and 221.

3.  If the first digit is 3, there are two ways to factor 3 using two
    integers, 1×3 = 3, and 3×1 = 3  so there are two multiple numbers with 1st
    digit 3, 313 and 331.

4.  If the first digit is 4, there are three ways to factor 4 using two
    integers, 1×4 = 4, 2×2 = 4 and 4×1 = 4  so there are two multiple numbers
    with 1st digit 3, 414, 422 and 441.

5.  If the first digit is 5, there are two ways to factor 5 using two
    integers, 1×5 = 5, and 5×1 = 5  so there are two multiple numbers with 1st
    digit 5, 515 and 551.

6.  If the first digit is 6, there are four ways to factor 6 using two
    integers, 1×6 = 6, 2×3 = 6, 3×2 = 6, and 661, so there are four multiple
    numbers with 1st digit 6, 616, 623, 632, and 661.

So there are 14 of them:

111, 212, 221, 313, 331, 414, 422, 441, 515, 551, 616, 623, 632, 661

Edwin
RELATED QUESTIONS

if the man age is in 3 digit. his age is equal to product of two number. one of the... (answered by Edwin McCravy)
A three-digit number is 13 times the product of its digits. The hundreds digit is larger (answered by MathLover1)
I am a three-digit number. I am an odd multiple of 50. The product of my first two digits (answered by Alan3354)
The sum of two digits of two digits number is 14.THe difference between the first and the (answered by josgarithmetic)
The sum of the two digits of a two digit number is 15 and the difference between the two... (answered by lwsshak3)
there is a two digit no. Such that sum of its digit is 6 while the product of digits (answered by ewatrrr)
What number is the greatest even two digit number whose product of its digits is... (answered by macston,solver91311)
The sum of the digits of a two digit number is 9. The number is twice the product of its... (answered by stanbon)
A two-digit number is 6 times its single digit. The sum of the digits is 6. Find the... (answered by ewatrrr,josgarithmetic)