What is the greatest number which divides 442, 569, 697 leaving remainder 1, 2 & 4 respectively
Answers
Step-by-step explanation:
We need to find the HCF of three number (442-1),(569-2),(697-4).
Hence,
442-1=441
569-2=567
697-4=693
441=3*3*7*7
567=3*3*3*3*7
693=3*3*7*11
HCF of (441,567,693)=63
Hence, the required number is 63.
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Answer: The greatest number which divides 442, 569, and 697 leaving a remainder of 1, 2, and 4 respectively is 1.
Let the greatest number which divides 442, 569 and 697 leaving a remainder of 1, 2 and 4 respectively be "n".
This means that we can write:
442 ≡ 1 (mod n) ...(1)
569 ≡ 2 (mod n) ...(2)
697 ≡ 4 (mod n) ...(3)
From equation (1), we can write:
441 = (n x q1) + 1
where q1 is some integer quotient.
From equation (2), we can write:
567 = (n x q2) + 2
where q2 is some integer quotient.
From equation (3), we can write:
693 = (n x q3) + 4
where q3 is some integer quotient.
Now, let's subtract equation (1) from equation (2):
127 = (n x (q2 - q1)) + 1
Since n is an integer, (q2 - q1) must also be an integer. This means that (127 - 1) must be divisible by n. Thus, we have:
126 = (n x (q2 - q1))
Similarly, we can subtract equation (2) from equation (3):
126 = (n x (q3 - q2))
Thus, we see that both 126 and 127 are divisible by n.
The greatest common divisor of 126 and 127 is 1, which means that n must be 1.
Therefore, the greatest number which divides 442, 569, and 697 leaving a remainder of 1, 2, and 4 respectively is 1.
Learn more about the greatest common divisor here
https://brainly.in/question/47392283ommon divisor here
Learn more about integer quotient here
https://brainly.in/question/54139217
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