The HCF of three distinct natural numbers is 11 and their sum is 209. How many ordered triplets satisfying this requirement exist?
183
153
126
110
Answers
Answer: 153
Step-by-step explanation:
Given : The HCF of three distinct natural numbers is 11
and their sum is 209
To Find : How many ordered triplets satisfying this requirement exist
Solution:
: The HCF of three distinct natural numbers is 11
Hence numbers can be
11a , 11b , 11c
11a + 11b +11c = 209
=> ( a + b + c) = 19
if a = 1 then b and c can take any 2 values adding to 18
hence 17 ways
if a = 2 then 16 ways
a = 3 then 15
a = 17 then 1 way
so total ways = 1 + 2 + 3 + ... + 17
= 17 * 9
= 153
Hence 153 ways
153 ordered triplets satisfying this requirement exist
Learn More:
Find LCM and HCF of the following pairs of integers and verify that ...
brainly.in/question/17387230
Can 12 and 98 be HCF and LCM of two numbers - Brainly.in
brainly.in/question/17564109