PHP loop learning eight: count the number of perfect numbers from 1 to 10,000, and output all perfect numbers

In the previous article "PHP Loop Learning 7: Two Methods to Print the 9*9 Quick Calculation Table", we introduced how to use the for loop and while loop to print the 99 multiplication table. Let's continue to understand the PHP loop and introduce the method of judging whether a given number is a complete number. Interested friends can learn about it~

First of all, let's understandWhat is a perfect number?

##Perfect number Full namePerfect number, if a number is exactly equal to the sum of its factors, then the number is called "perfect number" number". (Factors refer to divisors other than itself.)

For example: 6=1 2 3, 6 is a perfect number.

So if a number num (for example, 6) is given, how do we judge whether the number num is complete?

Idea:

1. Decompose the number num into factors, that is, find all the numbers that can divide num except itself. (This requires the use of loops).

We take the for loop as an example. Because 1 can divide any integer, the loop initial condition is set

i=1; and the divisor cannot be num itself, so the restriction condition is i<num. in this way the framework of for loop is rough><pre class='brush:php;toolbar:false;'>$num=6; for($i=1;$i&lt;$num;$i++){ if($num%$i==0){//分解因数 } }</pre></num.>

2. After finding the factors, you need to add these factors and sum them. This requires a variable $sum to receive the calculation result. Because it is addition, $sum can be initially assigned a value of 0.

$num=6;
$sum=0;
for($i=1;$i<$num;$i++){
    if($num%$i==0){//分解因数
        $sum=$sum+$i;  //各因数相加，求和
    }
}

3. Determine whether $sum and $num are equal. If they are equal, $num is a complete number.

The implementation code is given below:

Look at the output:

Now that we know how to determine whether a number is The count is not complete. Let’s increase the difficulty:

Output all the complete numbers in a given range (just 1~10000).

Analysis: There is a range of 1~10000, then we use a for loop to limit the range, so that a for loop is placed outside the above code:

<?php
header("Content-type:text/html;charset=utf-8");
for($a=1;$a<=10000;$a++){
	$sum=0;
	for($i=1;$i<$a;$i++){
	    if($a%$i==0){//分解因数
	        $sum=$sum+$i;  //各因数相加，求和
	    }
	}
	if($sum==$i){//如果这个数等于本身 则为完数
	echo "$i 是完数！<br>";
	}
}	
?>

See Look at the output:

#What if there are many given ranges and you want to know how many complete numbers there are? You can add a counter $b to the if statement. Every time a complete number is output, $b will increase by 1.

<?php
header("Content-type:text/html;charset=utf-8");
$b=0;
for($a=1;$a<=10000;$a++){
	$sum=0;
	for($i=1;$i<$a;$i++){
	    if($a%$i==0){//分解因数
	        $sum=$sum+$i;  //各因数相加，求和
	    }
	}
	if($sum==$i){//如果这个数等于本身 则为完数
	echo "$i 是完数！<br>";
	$b++;
	}
}
echo "<br>1~10000范围内有：$b 个完数。";
?>

Look at the output:

OK, done! All perfect numbers between 1 and 10,000 are output, and the number of perfect numbers is counted.

Okay, that’s all. If you want to know anything else, you can click this. → →

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