Page 141 - NUMINO Challenge_D2
P. 141
Answer Key
Number and Operations Problem solving
1 Prime Factorization p.8~p.9 1 The prime factorization of the given expression
Example 9, 3, 3, 36, 2, 5, 4, 9, 3, 3 is: 40 63 100 2 2 2 2 2 3 3 5 5
3, 3, 2, 3 5 7. In the expression, 2 is multiplied five
Try It Again 2, 2, 7 times, 3 is multiplied twice, 5 is multiplied three
even, 1, odd, 7 times, and 7 is multiplied once. To become a
7 square number, each prime number should be
multiplied an even number of times, therefore 2
TryItAgain The prime factorization of 135 is 3 3 3
5. To make 135 a square number, each 5 7 should be multiplied. Therefore, the
prime number of 135 should be multiplied smallest number that can make the given
an even number of times. Therefore 3 expression a square number is 2 5 7 70.
should be multiplied by itself four times and
5 should be multiplied by itself twice. 2 Among the square numbers that are greater than
Therefore, 135 becomes a square number
when it is multiplied by the smallest possible 100, the smallest number is 121 11 11. Among
number, which is 3 5 15. the square numbers smaller than 500, the
greatest number is 484 22 22. Therefore, the
square number greater than 100 but smaller than
500 is 11 11, 12 12, 13 13, , 20 20, 21
21, 22 22. There are 12 square numbers.
Type 1-2 The Number of Continuous 0's p.12~p.13
Type 1-1 Making a Square Number p.10~p.11 1 Number Prime Number Number Number
Factorization of 2's of 5's of 0's at the
1 36 2 2 3 3, 40 2 2 2 5
2 36 40 2 2 3 3 2 2 2 5 end
25 32 5 10 2 5 1 1 1
3 2, 5
4 10 100 2 2 5 5 2 2 2
1000 222 3 3 3
555
200 222 3 2 2
55
250 2 5 5 5 1 3 1
2 Whenever 2 and 5 are multiplied, there is one 0.
Therefore, the number of 0's is equal to the
number of 2's or 5's.
3 There are 20 multiples of 5.
4 There are 4 multiples of 25.
5 24 times
NUMINO Challenge D2
Number and Operations Problem solving
1 Prime Factorization p.8~p.9 1 The prime factorization of the given expression
Example 9, 3, 3, 36, 2, 5, 4, 9, 3, 3 is: 40 63 100 2 2 2 2 2 3 3 5 5
3, 3, 2, 3 5 7. In the expression, 2 is multiplied five
Try It Again 2, 2, 7 times, 3 is multiplied twice, 5 is multiplied three
even, 1, odd, 7 times, and 7 is multiplied once. To become a
7 square number, each prime number should be
multiplied an even number of times, therefore 2
TryItAgain The prime factorization of 135 is 3 3 3
5. To make 135 a square number, each 5 7 should be multiplied. Therefore, the
prime number of 135 should be multiplied smallest number that can make the given
an even number of times. Therefore 3 expression a square number is 2 5 7 70.
should be multiplied by itself four times and
5 should be multiplied by itself twice. 2 Among the square numbers that are greater than
Therefore, 135 becomes a square number
when it is multiplied by the smallest possible 100, the smallest number is 121 11 11. Among
number, which is 3 5 15. the square numbers smaller than 500, the
greatest number is 484 22 22. Therefore, the
square number greater than 100 but smaller than
500 is 11 11, 12 12, 13 13, , 20 20, 21
21, 22 22. There are 12 square numbers.
Type 1-2 The Number of Continuous 0's p.12~p.13
Type 1-1 Making a Square Number p.10~p.11 1 Number Prime Number Number Number
Factorization of 2's of 5's of 0's at the
1 36 2 2 3 3, 40 2 2 2 5
2 36 40 2 2 3 3 2 2 2 5 end
25 32 5 10 2 5 1 1 1
3 2, 5
4 10 100 2 2 5 5 2 2 2
1000 222 3 3 3
555
200 222 3 2 2
55
250 2 5 5 5 1 3 1
2 Whenever 2 and 5 are multiplied, there is one 0.
Therefore, the number of 0's is equal to the
number of 2's or 5's.
3 There are 20 multiples of 5.
4 There are 4 multiples of 25.
5 24 times
NUMINO Challenge D2
