Kinh Nghiệm về When a number is divided by 143 leaves remainder 31? Mới Nhất
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A number when divided by 143 leaves remainder 31. The remainder when the number is divided by 13 is [a] 0[b] 1[c] 3[d] 5
The number can be expessed by 143n+31 (euclid division lemma, a = bq+r) where n is any natural number.Now as 143 is divisible by 13, 143n leaves no remainer or zero as remainder when divided by 13.So we only need to focus on 31 now.31 divided by 13 leaves remainder 5Hence the answer is 5.When a number divided by 143 what is the remainder is 31?When divided by 143 leaves 31 as a reminder what will be the remainder when the same number is divided by 13?When divided by 114 leaves remainder 21 if the same number is divided by 19 then the remainder will be?What is divided by 4 leaves a remainder 3?
A number when divided by 143 leaves remainder 31. The remainder when the number is divided by 13 is [a] 0[b] 1[c] 3[d] 5
Answer
Verified
Hint: Let the number be n. Use Euclid's division lemma with a = n and b = 143. Write 31 as 26+5 and take 13 common from the first two terms. Hence find the remainder obtained on dividing by 13.
Alternatively, you can use the property that if $aequiv bbmod m$ and n divides m then $aequiv bbmod n$.
Use the fact that if $aequiv bbmod m$ thenn$aequiv b-cmbmod m$, where c is an integer.
Hence find the remainder on dividing by 13.
Complete step-by-step answer:
We know from
Euclid's division lemma if r is the remainder on dividing a by b then
a = bq+r.
Let n be the given number.
Hence n = 143q+31
Hence n = 143q+26+5
Taking 13 common from the first two terms, we get
n = 13(11q+2) +5
i.e. n = 13s+5 where s is an integer.
Since $0le 5<13$we have
The remainder on dividing n by 13 is 5.
Hence option [d] is correct.
Note: Let n be the given number.
Hence $nequiv 31bmod 143$
We know that if $aequiv bbmod m$ and n divides
m then $aequiv bbmod n$.
Since 13 divides 143, using the above property, we get
$beginalign
& nequiv 31bmod 13 \
& Rightarrow nequiv 5bmod 13 \
endalign$
Hence the remainder obtained on dividing the number by 13 is 5.
Hence option [d] is correct.
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A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13? (a) 0 (b) 1 (c) 3 (d) 5
A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13? (a) 0 (b) 1 (c) 3 (d) 5
Correct Answer: (d) 5
Explanation:
Dividend = Divisor × Quotient + Remainder.
Given,
Divisor = 143
Remainder = 13
The number is in the form of 143x + 31, where x is the quotient.
∴ 143x + 31 = 13 (11x) + (13 × 2) + 5 = 13 (11x + 2) + 5
The remainder will be 5 when the same number is divided by 13.
(d) 5
We know,
Dividend = Divisor × Quotient + Remainder.
It is given that:
Divisor = 143
Remainder = 13
So, the given number is in the form of 143x + 31, where x is the quotient.
∴ 143x + 31 = 13 (11x) + (13 × 2) + 5 = 13 (11x + 2) + 5
Thus, the remainder will be 5 when the same number is divided by 13.
Solution
The number can be expessed by 143n+31 (euclid division lemma, a = bq+r) where n is any natural number.Now as 143 is divisible by 13, 143n leaves no remainer or zero as remainder when divided by 13.So we only need to focus on 31 now.31 divided by 13 leaves remainder 5Hence the answer is 5.
When a number divided by 143 what is the remainder is 31?
It is given that: Divisor = 143 Remainder = 13 So the given number is in the form of 143x + 31 where x is the quotient. ∴ 143x + 31 = 13 11x + 13 × 2 + 5 = 13 11x + 2 + 5 Thus the remainder will be 5 when the same number is divided by 13. A number when divided by `143` leaves `31` as remainder.When divided by 143 leaves 31 as a reminder what will be the remainder when the same number is divided by 13?
Explanation: Dividend = Divisor × Quotient + Remainder. The number is in the form of 143x + 31, where x is the quotient. The remainder will be 5 when the same number is divided by 13.When divided by 114 leaves remainder 21 if the same number is divided by 19 then the remainder will be?
Hence, the remainder is 2.What is divided by 4 leaves a remainder 3?
Numbers which when divided by 4 that leave a remainder 3 are (4+3),(8+3),(12+3),(16+3),......,(296+3),(300+3),...... ( 4 + 3 ) , ( 8 + 3 ) , ( 12 + 3 ) , ( 16 + 3 ) , . . . . . . , ( 296 + 3 ) , ( 300 + 3 ) , . . . . . . Here, first number in the series is 7 and the last number is 299. Tải thêm tài liệu liên quan đến nội dung bài viết When a number is divided by 143 leaves remainder 31?