Page 20 - NUMINO Challenge_D2
P. 20
Basic Concepts Perfect Number
The divisors of a number, except for the number itself are proper divisors.
If the sum of all the proper divisors is less than the number itself, it is
called a deficient number; if the sum is equal to the number itself, it is
called a perfect number; if the sum is greater than the number itself, it is
called an abundant number. : deficient number
22 1 2 11 22
6 1236 : perfect number
12 1 2 3 4 6 12 : abundant number
If the product of the proper divisors is equal to the number itself, it is
called a product-perfect number.
1 2 3 6, 1 2 4 8
product-perfect
number
Example Classify the numbers 20 to 29 into deficient, perfect, and abundant
numbers.
Deficient number(s):
Perfect number(s):
Abundant number(s):
Class Notes
The proper divisors of 20 are 1, 2, 4, 5, and 10, and it is an abundant number, since
1 2 4 5 10 20. The proper divisors of 21 are 1, 3, and 7, and it is a deficient
number, since 1 3 7 21.
Use the method from to complete the table below.
Number Proper Divisors Sum Type of Number Proper Divisors Sum Type of
20 1, 2, 4, 5, 10 Numbers 1, 2, 13 Numbers
21 1, 3, 7
22 22 abundant 25
23 number
24
11 deficient 26 16 deficient
number number
27
28
29
Therefore, the deficient numbers from 20 to 29 are 21, 22, 23, 25, , , and
.
, the perfect number is , and the abundant numbers are 20 and
17Number and Operations
The divisors of a number, except for the number itself are proper divisors.
If the sum of all the proper divisors is less than the number itself, it is
called a deficient number; if the sum is equal to the number itself, it is
called a perfect number; if the sum is greater than the number itself, it is
called an abundant number. : deficient number
22 1 2 11 22
6 1236 : perfect number
12 1 2 3 4 6 12 : abundant number
If the product of the proper divisors is equal to the number itself, it is
called a product-perfect number.
1 2 3 6, 1 2 4 8
product-perfect
number
Example Classify the numbers 20 to 29 into deficient, perfect, and abundant
numbers.
Deficient number(s):
Perfect number(s):
Abundant number(s):
Class Notes
The proper divisors of 20 are 1, 2, 4, 5, and 10, and it is an abundant number, since
1 2 4 5 10 20. The proper divisors of 21 are 1, 3, and 7, and it is a deficient
number, since 1 3 7 21.
Use the method from to complete the table below.
Number Proper Divisors Sum Type of Number Proper Divisors Sum Type of
20 1, 2, 4, 5, 10 Numbers 1, 2, 13 Numbers
21 1, 3, 7
22 22 abundant 25
23 number
24
11 deficient 26 16 deficient
number number
27
28
29
Therefore, the deficient numbers from 20 to 29 are 21, 22, 23, 25, , , and
.
, the perfect number is , and the abundant numbers are 20 and
17Number and Operations
