Page 144 - NUMINO Challenge_D2
P. 144
Type 2-2 Finding the Unlocked Locker p.20~p.21 2 The 2-digit square numbers are 16, 25, 36, 49,
1 Locker 1 2 3 4 5 6 7 8 9 10 64, and 81. When the square numbers are prime
Number factored in order from greatest to smallest, the
number of factors is as shown below.
Student 81 3 3 3 3 34 Five Factors
Number 64 2 2 2 2 2 2 26 Seven Factors
49 7 7 72 Three Factors
2 A factor
Therefore, the greatest 2-digit number that has
3 A locker is open when the number of students three factors is 49.
written under the locker is an odd number. That
odd number is equal to the number of factors. Creative Thinking p.22~p.23
Therefore, lockers 1, 4, and 9 are open, and
each locker has an odd number of factors. 1 The given numbers are prime factored, and the
4 A square number number of their factors are shown below.
5 1, 4, 9, 16, 25, 36, 49 Number Prime Factorization Number of Factors
Problem solving 40 23 5 (3 1) (1 1) 8
54 2 33 (1 1) (3 1) 8
1 The number on the opened gate has an odd 98 2 72 (1 1) (2 1) 6
100 22 52 (2 1) (2 1) 9
number of factors, and the number that has an 200 23 52 (3 1) (2 1) 12
odd number of factors is a square number.
Among the numbers from 1 to 100, there are 2 8 1 2 4, 10 1 2 5, 14 1 2 7,
10 square numbers which are 1, 4, 9, 16, 25, 36,
49, 64, 81, and 100. Therefore, there are 10 15 1 3 5
gates that are opened.
3 Find the numbers that are divisible by their tens
The reason why a square number has an odd
number of factors: for example, the factors digit and ones digit.
of 36 can be found in the product of two 51~59: 55 (also divisible by 5)
numbers, such as in 1 36 and 2 18. In 6 60~69: 60, 66 (also divisible by 6)
6 36, only one of the two 6's is counted as 70~79: 70, 77 (also divisible by 7)
a factor; therefore, a square number has an 80~89: 80, 88 (also divisible by 8)
odd number of factors. 90~99: 90, 99 (also divisible by 9)
Therefore, there are 9 numbers in which the
factors are divisible.
55, 60, 66, 70, 77, 80, 88, 90, 99
Answer Key
1 Locker 1 2 3 4 5 6 7 8 9 10 64, and 81. When the square numbers are prime
Number factored in order from greatest to smallest, the
number of factors is as shown below.
Student 81 3 3 3 3 34 Five Factors
Number 64 2 2 2 2 2 2 26 Seven Factors
49 7 7 72 Three Factors
2 A factor
Therefore, the greatest 2-digit number that has
3 A locker is open when the number of students three factors is 49.
written under the locker is an odd number. That
odd number is equal to the number of factors. Creative Thinking p.22~p.23
Therefore, lockers 1, 4, and 9 are open, and
each locker has an odd number of factors. 1 The given numbers are prime factored, and the
4 A square number number of their factors are shown below.
5 1, 4, 9, 16, 25, 36, 49 Number Prime Factorization Number of Factors
Problem solving 40 23 5 (3 1) (1 1) 8
54 2 33 (1 1) (3 1) 8
1 The number on the opened gate has an odd 98 2 72 (1 1) (2 1) 6
100 22 52 (2 1) (2 1) 9
number of factors, and the number that has an 200 23 52 (3 1) (2 1) 12
odd number of factors is a square number.
Among the numbers from 1 to 100, there are 2 8 1 2 4, 10 1 2 5, 14 1 2 7,
10 square numbers which are 1, 4, 9, 16, 25, 36,
49, 64, 81, and 100. Therefore, there are 10 15 1 3 5
gates that are opened.
3 Find the numbers that are divisible by their tens
The reason why a square number has an odd
number of factors: for example, the factors digit and ones digit.
of 36 can be found in the product of two 51~59: 55 (also divisible by 5)
numbers, such as in 1 36 and 2 18. In 6 60~69: 60, 66 (also divisible by 6)
6 36, only one of the two 6's is counted as 70~79: 70, 77 (also divisible by 7)
a factor; therefore, a square number has an 80~89: 80, 88 (also divisible by 8)
odd number of factors. 90~99: 90, 99 (also divisible by 9)
Therefore, there are 9 numbers in which the
factors are divisible.
55, 60, 66, 70, 77, 80, 88, 90, 99
Answer Key
