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Answer the following : (2 mark each)

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50 questions · timed · auto-graded

Question 12 Marks
Give an example to show that every non-zero number is a factor of $0.$(Hint: $0 \div 5 = 0,$ but division by $0$ is not defined.)
Answer
$0 = 1 \times 0 = 2 \times 0 3 \times 0 = ….$
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Question 22 Marks
Reva counted $7$ notes of $₹20$ equal to $₹140.$ Are $7$ and $20$ the factors of $140?$ If yes write other factors of $140.$
Answer
Yes; $1, 2, 4, 5, 10, 14, 28, 35, 70, 140$
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Question 32 Marks
The numbers $17$ and $71$ are prime numbers having the same digits. Find two more such pairs.
Answer
$13$ and $31;37$ and $73$
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Question 42 Marks
Build a number that has exactly four different prime factors.
Answer
$2 \times 3 \times 5 \times 7 = 210$
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Question 102 Marks
Find the first three common multiples of $(a) \ 2$ and $3 \ (b) \ 6$ and $8.$
Answer
$(a) \ 6, 12, 18$
$(b) \ 24, 48, 72$
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Question 122 Marks
Without actual division, tick (✔) the numbers that are divisible by $6.$
$46\ 216\ 126\ 154\ 308$
Answer
$216, 126$
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Question 132 Marks
Tell without actual division that $2, 4, 5, 6, 8$ and $10$ are not factors of $219.$
Answer
$219$ is odd but $2, 4, 6, 8$ and $10$ are even so these are not factors of $219.$ Further, $219$ has ones digit $9,$ so, $219$ is not a factor of $5.$
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Question 142 Marks
If a number is divisible by $9,$ then is it necessary to check its divisibility by $3?$ If not, why?
Answer
No, as $3$ is a factor of $9.$
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Question 162 Marks
List the factors of $10$ and $25.$ What factors are common to both the numbers?
Answer
Factors of $10$ are $1, 2, 5,$ and $10$. Factors of $25$ are $1, 5$ and $25$. Common factors of $10$ and $25$ are $1$ and $5.$
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Question 232 Marks
Write all the factor pairs of: $216$
Answer
$(1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), (12, 18)$
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Question 272 Marks
Encircle the even numbers and cross out the odd numbers: $16, 150, 193, 301, 43295, 1659, 1007, 568, 9994$
Answer
Even numbers: $16, 150, 568, 9994;$
Odd numbers: $193, 301, 43295, 1659, 1007$
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Question 322 Marks
Find the prime factorisation: $512$
Answer
$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
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Question 402 Marks
Obtain the factorisation by $(i)$ factor tree method and $(ii)$ division method.: $765$
Answer
$765 = 3 \times 3 \times 5 \times 17$
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Question 412 Marks
Obtain the factorisation by $(i)$ factor tree method and $(ii)$ division method.: $400$
Answer
$400 = 2 \times 2 \times 2 \times 2 \times 5 \times 5$
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Question 422 Marks
Obtain the factorisation by $(i)$ factor tree method and $(ii)$ division method.: $250$
Answer
$250 = 2 \times 5 \times 5 \times 5$
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Question 432 Marks
Obtain the factorisation by $(i)$ factor tree method and $(ii)$ division method.: $63$
Answer
$63 = 3 \times 3 \times 7$
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Question 442 Marks
Obtain the factorisation by $(i)$ factor tree method and $(ii)$ division method.: $36$
Answer
$36 = 2 \times 2 \times 3 \times 3$
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Answer the following : (2 mark each) - MATH-MAGIC STD 4 Questions - Vidyadip