Page 143 - NUMINO Challenge_D2
P. 143
Answer
Key
2 Factors p.16~p.17 Type 2-1 Number of Factors p.18~p.19
Example 2, 3, 3 1 9 1 9 (0 1) (8 1)
m 0, n 8 or m 8, n 0
1 2 22 23
1 1 1 1 1 2 2 1 22 4 1 23 8 9 3 3 (2 1) (2 1)
3 3 1 3 3 2 6 3 22 12 3 23 24 m 2, n 2
32 32 1 9 32 2 18 32 22 36 32 23 72
22
9, 12, 18, 24, 36, 72, 12
3 A=2, B=3 or A=3, B=2
TryItAgain The exponents of the prime numbers of 36
are shown below. 4 If m 8 and n 0 (or m 0 and n 8),
28 1 256.
1 2 22 If m 2 and n 2, 22 32 36.
1124 Therefore, the smallest number is 36.
3 3 6 12
32 9 18 36 Problem solving
Therefore, the total number of factors of 36 1 If a number is prime factored and represented in
is (2+1) (2+1) 9.
the form of Am Bn, the number of factors is
Example (m 1) (n 1).
When there are four factors, m 3 and n 0, or
Number Proper Divisors Sum Type of m 1 and n 1.
Numbers
20 1, 2, 4, 5, 10 If m 3 and n 0 (or m 0 and n 3),
22 Abundant 23 8 and 33 27, therefore A can be either 2
Number or 3. Therefore, among the numbers from 1 to
30, the numbers that have four factors are 8
21 1, 3, 7 11 Deficient and 27.
22 1, 2, 11 Number If m 1 and n 1,
2 3 6, 2 5 10, 2 7 14, 2 11 22,
14 Deficient 2 13 26, 3 5 15, 3 7 21. Therefore,
Number among the numbers from 1 to 30, the numbers
that have four factors are 6, 10, 14, 22, 26, 15,
23 1 1 Deficient and 21.
24 1, 2, 3, 4, 6, 8, 12 Number 6, 8, 10, 14, 15, 21, 22, 26, 27
36 Abundant 2 A number that has exactly two factors is a prime
Number number. Since 589 is an odd number, an even
prime number and an odd prime number must be
25 1, 5 6 Deficient added. The only even prime number is 2, therefore
Number the two prime numbers are 2 and 587.
26 1, 2, 13 16 Deficient
Number
27 1, 3, 9 13 Deficient
Number
28 1, 2, 4, 7, 14 28 Abundant
Number
29 1 1 Deficient
Number
26, 27, 29, 28, 24
NUMINO Challenge D2
Key
2 Factors p.16~p.17 Type 2-1 Number of Factors p.18~p.19
Example 2, 3, 3 1 9 1 9 (0 1) (8 1)
m 0, n 8 or m 8, n 0
1 2 22 23
1 1 1 1 1 2 2 1 22 4 1 23 8 9 3 3 (2 1) (2 1)
3 3 1 3 3 2 6 3 22 12 3 23 24 m 2, n 2
32 32 1 9 32 2 18 32 22 36 32 23 72
22
9, 12, 18, 24, 36, 72, 12
3 A=2, B=3 or A=3, B=2
TryItAgain The exponents of the prime numbers of 36
are shown below. 4 If m 8 and n 0 (or m 0 and n 8),
28 1 256.
1 2 22 If m 2 and n 2, 22 32 36.
1124 Therefore, the smallest number is 36.
3 3 6 12
32 9 18 36 Problem solving
Therefore, the total number of factors of 36 1 If a number is prime factored and represented in
is (2+1) (2+1) 9.
the form of Am Bn, the number of factors is
Example (m 1) (n 1).
When there are four factors, m 3 and n 0, or
Number Proper Divisors Sum Type of m 1 and n 1.
Numbers
20 1, 2, 4, 5, 10 If m 3 and n 0 (or m 0 and n 3),
22 Abundant 23 8 and 33 27, therefore A can be either 2
Number or 3. Therefore, among the numbers from 1 to
30, the numbers that have four factors are 8
21 1, 3, 7 11 Deficient and 27.
22 1, 2, 11 Number If m 1 and n 1,
2 3 6, 2 5 10, 2 7 14, 2 11 22,
14 Deficient 2 13 26, 3 5 15, 3 7 21. Therefore,
Number among the numbers from 1 to 30, the numbers
that have four factors are 6, 10, 14, 22, 26, 15,
23 1 1 Deficient and 21.
24 1, 2, 3, 4, 6, 8, 12 Number 6, 8, 10, 14, 15, 21, 22, 26, 27
36 Abundant 2 A number that has exactly two factors is a prime
Number number. Since 589 is an odd number, an even
prime number and an odd prime number must be
25 1, 5 6 Deficient added. The only even prime number is 2, therefore
Number the two prime numbers are 2 and 587.
26 1, 2, 13 16 Deficient
Number
27 1, 3, 9 13 Deficient
Number
28 1, 2, 4, 7, 14 28 Abundant
Number
29 1 1 Deficient
Number
26, 27, 29, 28, 24
NUMINO Challenge D2
