The sum of two numbers is 363 and their hcf is 33, how many such pairs are there in all
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we assume the two given numbers are positive integers.
a + b = 363 and HCF(a, b) = 33
Let a = 33 * m, m is a positive integer
b= 33 * n , n is a positive integer
a + b = 33 ( m + n) = 363
m + n = 11
As m and n are >= 1, the solutions (m, n) are
(1, 10), (2, 9) , (3, 8) ..... (10, 1)
that is a and b can be
(33, 330), (66, 297), (99, 264), .... (330, 33)
there are ten such pairs.
If the numbers can be negative, then you have many such combinations.
a + b = 363 and HCF(a, b) = 33
Let a = 33 * m, m is a positive integer
b= 33 * n , n is a positive integer
a + b = 33 ( m + n) = 363
m + n = 11
As m and n are >= 1, the solutions (m, n) are
(1, 10), (2, 9) , (3, 8) ..... (10, 1)
that is a and b can be
(33, 330), (66, 297), (99, 264), .... (330, 33)
there are ten such pairs.
If the numbers can be negative, then you have many such combinations.
mathskhongstid:
Very helpful, thanks
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