The sum of two numbers is 156 and their HCF is 26. Find how many such pairs can be formed.
If HCF of two numbers is 26, then the two numbers are 26X & 26Y where X & Y are co-prime numbers. ⇒ H.C.F(X,Y) = 1 Now the sum of the two numbers is 156. So we can say, 26X + 26Y = 156 ⇒ X + Y = 6 The possible pairs of X & Y are: (1, 5), (2, 4), (3, 3), (5, 1), (4, 2) [As we are not considering the ordered pairs (2, 4), (4, 2), (3, 3) because X and Y are coprime] Accepted possible pairs of X & Y are: (1, 5), (5, 1) Such a number of pairs, For (1, 5) => 26, (26 × 5) = 130 For (5, 1) => (26 × 5) = 130, 26 Combining the above results, So, there will be only one pair of numbers which will give the sum of two numbers is 156 and their HCF is 16 and that pair of the numbers will be (26, 130) only.
Which of the following statements correctly describes the situation and measures taken by Gujarat in response to the Chandipura virus (CHPV) outbreak?
Who was the runner-up in the women's final of the 2024 French Open?
What is Fitch Ratings' revised growth forecast for India for FY25?
The Ministry of Fisheries, Animal Husbandry & Dairying has released the Basic Animal Husbandry Statistics 2023 (milk, egg, meat and wool production 2022...
Which bank has opened its fourth branch for start-ups in Mumbai to provide end-to-end support at every stage of their journey, starting from the form...
Where did Indian Renewable Energy Development Agency Limited (IREDA) organize its 16th Stakeholders' Interaction Meet?
Who has been nominated as the ambassador for the "War Against Waste" initiative in Jammu & Kashmir, as announced by the Directorate of Rural Sanitation,...
Recently SIDBI signed an MoU with which state government to set up Project Management Units (PMU) in the state?
The Reserve Bank of India (RBI) has announced that the Unified Payments Interface (UPI) payment limit for hospitals and educational institutions would b...
How many gallantry awards have been approved by the President on the occasion of 77th Independence Day?