Find all possible pairs of two natural numbers whose sum is 77 and their g.c.d. is 7
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Sum of two natural consecutive no. is77 & g.c.d is 7 then find other pairs.
7'70
To find all possible pairs of two natural numbers whose sum is 77 and their greatest common divisor (gcd) is 7, we can follow these steps:
Step 1: Determine the factors of 7
Since the gcd of the two numbers is 7, this means both numbers are divisible by 7. The factors of 7 are 1 and 7.
Step 2: Find all possible combinations
To find all pairs of numbers whose sum is 77 and gcd is 7, we need to consider all possible combinations of numbers that are multiples of 7 and add up to 77.
Let's list down the multiples of 7 that are less than or equal to 77:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
Now, we need to find pairs of numbers whose sum is 77. To do this, we can iterate through all the multiples of 7 and check if their complement (77 minus the multiple) is also a multiple of 7.
Pairs:
7 + 70 = 77 (7 * 1, 7 * 10)
14 + 63 = 77 (7 * 2, 7 * 9)
21 + 56 = 77 (7 * 3, 7 * 8)
28 + 49 = 77 (7 * 4, 7 * 7)
35 + 42 = 77 (7 * 5, 7 * 6)
So, the possible pairs of two natural numbers whose sum is 77 and gcd is 7 are:
(7, 70), (14, 63), (21, 56), (28, 49), (35, 42)