Page 142 - NUMINO Challenge_D2
P. 142
6 24 2 If 2 is multiplied by itself once, twice, three
Problem solving times, four times, and so on, the digits in the
ones place of the product repeat in the order of
1 In the expression, 2 is multiplied five times, 3 is 2, 4, 8, and 6. If 7 is multiplied by itself once,
twice, three times, four times, and so on, the
multiplied seven times, 5 is multiplied ten times, digits in the ones place of the product repeat in
and 7 is multiplied six times. Between 2 and 5, 2 the order of 7, 9, 3, and 1. If 2 is multiplied by
is being multiplied fewer times than 5. Therefore itself a multiple of four times, the product ends
there will be five 0's at the end, which is equal to in 6, therefore 220 ends in 6. Also, if 7 is multiplied
the number of times 2 is multiplied by. Therefore, by itself a multiple of four times, the product
the result can be divided by 10 five times. ends in 1, therefore 720 ends in 1. Therefore, the
product of 220 has the greater digit in the ones
2 10 20 30 80 90 100 place.
10 (2 10) (3 10) (9 10) (10 10) 3 The prime factorization is: 12 63 2 2 3 3
(1 2 3 8 9 10) 3 7. To be a square number, each prime
number must be multiplied an even number of
Multiple of 5: 2 times. Since 2 is multiplied twice, three is
multiplied 3 times, and seven is multiplied once,
(10 10 10 10 10 10) you can divide once by 8 and 7 to make the
result a square number. Therefore, when you
Number of 10: 10 divide the product of 12 63 by 21, the result
Therefore, the number of continuous 0's at the becomes a square number, 36.
end of the result is 12.
4 You need to find how many times 2 and 5 are
Creative Thinking p.14~p.15
multiplied among numbers from 50 to 100. But
1 The factor trees of the given numbers are as in the multiplication of consecutive numbers, 5
is multiplied fewer times than 2, therefore the
shown below. number of 0's is equal to the number of 5's that
is multiplied. In the multiples of 25, 5 is
108 2 2 3 3 3 280 2 2 2 5 7 multiplied twice, therefore 5 is multiplied one
more time than other multiples of 5. Among
22 33 23 5 7 numbers from 50 to 100, the number of
multiples of 5 is 11, and the number of multiples
of 25 is 3. Therefore, 5 is multiplied 11 3 14
times, therefore there are 14 0's at the end.
Answer Key
Problem solving times, four times, and so on, the digits in the
ones place of the product repeat in the order of
1 In the expression, 2 is multiplied five times, 3 is 2, 4, 8, and 6. If 7 is multiplied by itself once,
twice, three times, four times, and so on, the
multiplied seven times, 5 is multiplied ten times, digits in the ones place of the product repeat in
and 7 is multiplied six times. Between 2 and 5, 2 the order of 7, 9, 3, and 1. If 2 is multiplied by
is being multiplied fewer times than 5. Therefore itself a multiple of four times, the product ends
there will be five 0's at the end, which is equal to in 6, therefore 220 ends in 6. Also, if 7 is multiplied
the number of times 2 is multiplied by. Therefore, by itself a multiple of four times, the product
the result can be divided by 10 five times. ends in 1, therefore 720 ends in 1. Therefore, the
product of 220 has the greater digit in the ones
2 10 20 30 80 90 100 place.
10 (2 10) (3 10) (9 10) (10 10) 3 The prime factorization is: 12 63 2 2 3 3
(1 2 3 8 9 10) 3 7. To be a square number, each prime
number must be multiplied an even number of
Multiple of 5: 2 times. Since 2 is multiplied twice, three is
multiplied 3 times, and seven is multiplied once,
(10 10 10 10 10 10) you can divide once by 8 and 7 to make the
result a square number. Therefore, when you
Number of 10: 10 divide the product of 12 63 by 21, the result
Therefore, the number of continuous 0's at the becomes a square number, 36.
end of the result is 12.
4 You need to find how many times 2 and 5 are
Creative Thinking p.14~p.15
multiplied among numbers from 50 to 100. But
1 The factor trees of the given numbers are as in the multiplication of consecutive numbers, 5
is multiplied fewer times than 2, therefore the
shown below. number of 0's is equal to the number of 5's that
is multiplied. In the multiples of 25, 5 is
108 2 2 3 3 3 280 2 2 2 5 7 multiplied twice, therefore 5 is multiplied one
more time than other multiples of 5. Among
22 33 23 5 7 numbers from 50 to 100, the number of
multiples of 5 is 11, and the number of multiples
of 25 is 3. Therefore, 5 is multiplied 11 3 14
times, therefore there are 14 0's at the end.
Answer Key
