C Program to Find All Factors of a Number
C Program to Find All Factors of a Number
A teacher wants every equal grouping size for twelve students. A grouping size works when division leaves no remainder.
A positive factor of n divides n exactly; enumerate candidates and keep those whose integer remainder is zero.
Before this exercise, review loops and stopping conditions and functions and parameters. The worked program below applies those ideas to this specific problem.
Explain
Explain why all factors uses this sequence of operations.
Trace
Trace the sample values and predict the printed result.
Apply
List the factors of seven.
All Factors: follow the data
Given data
A teacher wants every equal grouping size for twelve students. A grouping size works when division leaves no remainder.
Rule
A positive factor of n divides n exactly; enumerate candidates and keep those whose integer remainder is zero.
Observed result
1 2 3 4 6 12
Understand the operation
One and n are included for every positive n. A prime has only those two factors, while a composite also has factors between them.
This complete first approach scans every candidate in increasing order. A square-root approach can emit factor pairs faster, but must avoid duplicating a square root and preserve any promised output order.
Read the complete C program
The input values are written into this complete C17 example so the calculation can be reproduced without an unavailable service. Change the named data, rebuild and compare the actual output with your prediction.
C17 · complete program
#include <stdio.h>
int main(void) {
int number = 12;
for (int divisor = 1; divisor <= number; divisor++) {
if (number % divisor == 0) printf("%d ", divisor);
}
putchar('\n');
return 0;
}
Expected output
1 2 3 4 6 12
Follow the values through the code
C17 · code used in this explanation
#include <stdio.h>
int main(void) {
int number = 12;
for (int divisor = 1; divisor <= number; divisor++) {
if (number % divisor == 0) printf("%d ", divisor);
}
putchar('\n');
return 0;
}
The candidates run from one through twelve.
Remainder-zero candidates are 1, 2, 3, 4, 6 and 12, printed in increasing order.
Follow the worked calculation
Start with the sample
The candidates run from one through twelve.
Apply the rule
Remainder-zero candidates are 1, 2, 3, 4, 6 and 12, printed in increasing order.
Check the result
1 2 3 4 6 12
1 2 3 4 6 12
Try a small variation
C17 · code used in this explanation
#include <stdio.h>
int main(void) {
int number = 12;
for (int divisor = 1; divisor <= number; divisor++) {
if (number % divisor == 0) printf("%d ", divisor);
}
putchar('\n');
return 0;
}
List the factors of seven.
Worked answer
Only one and seven divide the prime input exactly, so the output has two factors.
C17 · complete program
#include <stdio.h>
int main(void) {
int number = 7;
for (int divisor = 1; divisor <= number; divisor++) {
if (number % divisor == 0) printf("%d ", divisor);
}
putchar('\n');
return 0;
}
Expected output
1 7
Recognize the important boundaries
Zero is not within this positive-natural-number contract; every nonzero integer divides zero, so a finite 1-through-n scan is not the same problem.
A loop through the maximum signed integer can overflow its counter after the last value. Bound user input or use a termination form that avoids that increment.
Check your understanding
Choose the answer, then compare the reasoning for every option.
Use the idea independently
A positive factor of n divides n exactly; enumerate candidates and keep those whose integer remainder is zero.
Continue with testing the problem’s boundary cases.
Language reference: WG14 C11 committee draft. These examples use the C17-compatible subset of the explained language features.
Reaching the recap and completing the quizzes are separate milestones.