The sum of two numbers is 156 and their hcf is 13. The numbers of such number pairs is
Answers
Answer:
2
Step-by-step explanation:
(65,91) and (13,143)
First, find the multiples of 13, upto 156.
Then group the numbers from the extreme ends, moving towards the center.
(0,156),(13,143), (26,130), (39,117), (52,104), (65,91), (78,78)
Factorize each set and see whose HCF is 13.
The required pairs are: i) 13 and 143 or ii) 65 and 91
Step-by-step explanation:
Consider the provided information.
HCF of the two numbers are 13.
Lets say two numbers are: 13A and 13B
Where A and B are co-prime numbers
Therefore, HCF of A and B = 1
The sum of two numbers is 156
13A + 13B = 156
13(A + B) = 156
A + B = 12
Thus, the possible case are:
1 + 11 = 12
2 + 10 = 12 (2 and 10 are not co-prime)
3 + 9 = 12 (3 and 9 are not co-prime)
4 + 8 = 12 (4 and 8 are not co-prime)
5 + 7 = 12
6 + 6 = 12 (6 and 6 are not co-prime)
For A=1 and B=11
13×1=13 and 13×11=143
For A=5 and B=7
13×5=65 and 13×7=91
Hence, the required pairs are: i) 13 and 143 or ii) 65 and 91
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