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A number when divided by 703 gives a remainder of 75. What will be the remainder when we divide the same number by 37?
- a)1
- b)2
- c)5
- d)7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A number when divided by 703 gives a remainder of 75. What will be the...
Let the number be N and its quotient be k.
Then the number N can be written in the form of:
N = 703k + 75
Now, we have to find out the what will be the remainder when it is divided by 37.
The number is (703k + 75)
Let’s divide it by 37
(703k + 75)/ 37
703 is divisible by 37 hence, remainder will be 0 whereas, 75 when divided by 37 leaves remainder 1.
Therefore, the remainder when the number N is divided by 37 will be (0+1) i.e. 1.
Then the number N can be written in the form of:
N = 703k + 75
Now, we have to find out the what will be the remainder when it is divided by 37.
The number is (703k + 75)
Let’s divide it by 37
(703k + 75)/ 37
703 is divisible by 37 hence, remainder will be 0 whereas, 75 when divided by 37 leaves remainder 1.
Therefore, the remainder when the number N is divided by 37 will be (0+1) i.e. 1.
Most Upvoted Answer
A number when divided by 703 gives a remainder of 75. What will be the...
Let the number be N and its quotient be k.
Then the number N can be written in the form of:
N = 703k + 75
Now, we have to find out the what will be the remainder when it is divided by 37.
The number is (703k + 75)
Let’s divide it by 37
(703k + 75)/ 37
703 is divisible by 37 hence, remainder will be 0 whereas, 75 when divided by 37 leaves remainder 1.
Therefore, the remainder when the number N is divided by 37 will be (0 + 1) i.e. 1.
Then the number N can be written in the form of:
N = 703k + 75
Now, we have to find out the what will be the remainder when it is divided by 37.
The number is (703k + 75)
Let’s divide it by 37
(703k + 75)/ 37
703 is divisible by 37 hence, remainder will be 0 whereas, 75 when divided by 37 leaves remainder 1.
Therefore, the remainder when the number N is divided by 37 will be (0 + 1) i.e. 1.
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Community Answer
A number when divided by 703 gives a remainder of 75. What will be the...
To solve this problem, we can use the concept of modular arithmetic.
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus. In this case, the modulus is 703.
Let's denote the number we are dividing as N. We are given that dividing N by 703 gives a remainder of 75. We can express this as:
N ≡ 75 (mod 703)
To find the remainder when N is divided by 37, we need to find N ≡ ? (mod 37).
To solve this, we can use the property of congruence that states if a ≡ b (mod m), then a ≡ b + km (mod m) for any integer k.
In our case, we can add or subtract multiples of 703 to the left side of the congruence equation without changing its value. We can subtract multiples of 703 to make the left side smaller and more manageable.
Let's subtract 703 from both sides of the equation:
N - 703 ≡ 75 - 703 (mod 703)
Simplifying:
N - 703 ≡ -628 (mod 703)
Now, we can rewrite -628 as a positive number that is congruent to it modulo 703. We can add 703 to -628 until we get a positive value:
-628 + 703 ≡ 75 (mod 703)
So, we have:
N - 703 ≡ 75 (mod 703)
N ≡ 75 + 703 ≡ 778 (mod 703)
Now, we can find the remainder when N is divided by 37:
N ≡ 778 (mod 37)
To simplify this congruence, we can divide 778 by 37:
778 ÷ 37 = 21 remainder 1
Therefore, the remainder when N is divided by 37 is 1.
Hence, the correct answer is option A) 1.
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus. In this case, the modulus is 703.
Let's denote the number we are dividing as N. We are given that dividing N by 703 gives a remainder of 75. We can express this as:
N ≡ 75 (mod 703)
To find the remainder when N is divided by 37, we need to find N ≡ ? (mod 37).
To solve this, we can use the property of congruence that states if a ≡ b (mod m), then a ≡ b + km (mod m) for any integer k.
In our case, we can add or subtract multiples of 703 to the left side of the congruence equation without changing its value. We can subtract multiples of 703 to make the left side smaller and more manageable.
Let's subtract 703 from both sides of the equation:
N - 703 ≡ 75 - 703 (mod 703)
Simplifying:
N - 703 ≡ -628 (mod 703)
Now, we can rewrite -628 as a positive number that is congruent to it modulo 703. We can add 703 to -628 until we get a positive value:
-628 + 703 ≡ 75 (mod 703)
So, we have:
N - 703 ≡ 75 (mod 703)
N ≡ 75 + 703 ≡ 778 (mod 703)
Now, we can find the remainder when N is divided by 37:
N ≡ 778 (mod 37)
To simplify this congruence, we can divide 778 by 37:
778 ÷ 37 = 21 remainder 1
Therefore, the remainder when N is divided by 37 is 1.
Hence, the correct answer is option A) 1.
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A number when divided by 703 gives a remainder of 75. What will be the remainder when we divide the same number by 37?a)1b)2c)5d)7Correct answer is option 'A'. Can you explain this answer?
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