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What is the remainder when 1044 × 1047 × 1050 × 1053 is divided by 33?
- a)3
- b)27
- c)30
- d)21
- e)18
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
What is the remainder when 1044 × 1047 × 1050 × 1053...
Useful result pertaining to remainders
You can solve this problem if you know this rule about remainders.
Let a number x divide the product of A and B.
The remainder will be the product of the remainders when x divides A and when x divides B.
Let a number x divide the product of A and B.
The remainder will be the product of the remainders when x divides A and when x divides B.
Using this rule,
The remainder when 33 divides 1044 is 21.
The remainder when 33 divides 1047 is 24.
The remainder when 33 divides 1050 is 27.
The remainder when 33 divides 1053 is 30.
The remainder when 33 divides 1044 is 21.
The remainder when 33 divides 1047 is 24.
The remainder when 33 divides 1050 is 27.
The remainder when 33 divides 1053 is 30.
∴ the remainder when 33 divides 1044 × 1047 × 1050 × 1053 is 21 × 24 × 27 × 30.
Note: The remainder when a number is divided by a divisor 'd' will take values from 0 to (d - 1). It will not be equal to or more than 'd'
The value of 21 × 24 × 27 × 30 is more than 33.
When the value of the remainder is more than the divisor, the final remainder will be the remainder of dividing the product by the divisor.
i.e., the final remainder is the remainder when 33 divides 21 × 24 × 27 × 30.
When 33 divides 21 × 24 × 27 × 30, the remainder is 30.
When the value of the remainder is more than the divisor, the final remainder will be the remainder of dividing the product by the divisor.
i.e., the final remainder is the remainder when 33 divides 21 × 24 × 27 × 30.
When 33 divides 21 × 24 × 27 × 30, the remainder is 30.
Choice C is the correct answer.
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Community Answer
What is the remainder when 1044 × 1047 × 1050 × 1053...
Solution:
Step 1: Find the remainders of each number when divided by 33
- 1044 divided by 33 leaves a remainder of 12
- 1047 divided by 33 leaves a remainder of 15
- 1050 divided by 33 leaves a remainder of 18
- 1053 divided by 33 leaves a remainder of 21
Step 2: Multiply the remainders
12 x 15 x 18 x 21 = 113400
Step 3: Find the remainder when 113400 is divided by 33
113400 divided by 33 leaves a remainder of 30
Therefore, the remainder when 1044 x 1047 x 1050 x 1053 is divided by 33 is 30. So, the correct answer is option C.
Step 1: Find the remainders of each number when divided by 33
- 1044 divided by 33 leaves a remainder of 12
- 1047 divided by 33 leaves a remainder of 15
- 1050 divided by 33 leaves a remainder of 18
- 1053 divided by 33 leaves a remainder of 21
Step 2: Multiply the remainders
12 x 15 x 18 x 21 = 113400
Step 3: Find the remainder when 113400 is divided by 33
113400 divided by 33 leaves a remainder of 30
Therefore, the remainder when 1044 x 1047 x 1050 x 1053 is divided by 33 is 30. So, the correct answer is option C.
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What is the remainder when 1044 × 1047 × 1050 × 1053 is divided by 33?a)3b)27c)30d)21e)18Correct answer is option 'C'. Can you explain this answer?
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