# Tag Archives: divisibility rules

## Divisible by 7

How many four digit positive integers divisible by have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by ? Source: NCTM Mathematics Teacher, October 2006 Solution Is … Continue reading

## Multiple of 72

The seven-digit integer is a multiple of (where are digits). Determine all possible ordered pairs . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Since and , we multiply by , etc. and by , etc. to find the possible digits … Continue reading

## Prime Number

What is the last digit of the 9-digit number , given that the number is prime? Source: NCTM Mathematics Teacher, November 2006 SOLUTION The last digit could be , or . cannot be because . cannot be because . cannot be … Continue reading

## Ends in 75

Determine how many positive whole numbers exist that meet all of the following conditions: 1. Greater than one thousand 2. Less than ten thousand 3. End in seventy-five 4. Divisible by seventy-five. Source: mathcontest.olemiss.edu 10/15/2007 SOLUTION Condition 1 and 2 … Continue reading

## Divisibility Rules

A nine-digit number consists of each digit from 1 to 9 and the nine-digit number is divisible by 9. If you remove the rightmost digit, the remaining eight-digit number will be divisible by eight. If you remove the next rightmost … Continue reading