Mathematics
Fill in the blanks:
(i) HCF of two consecutive natural numbers is ….
(ii) HCF of two consecutive odd numbers is ….
(iii) HCF of two consecutive even numbers is ….
Answer
(i) Two consecutive natural numbers do not share any common factor other than 1.
Hence, HCF of two consecutive natural numbers is 1.
(ii) Two consecutive odd numbers (e.g., 5 and 7, or 9 and 11) have no common factor other than 1.
Hence, HCF of two consecutive odd numbers is 1.
(iii) Two consecutive even numbers (e.g., 6 and 8, or 10 and 12) are both divisible by 2, but not by any other common factor.
Hence, HCF of two consecutive even numbers is 2.
Related Questions
Find the HCF of the given numbers by prime factorisation method:
(i) 28, 36
(ii) 54, 72, 90
(iii) 105, 140, 175
Find the HCF of the given numbers by division method:
(i) 198, 429
(ii) 20, 64, 104
(iii) 120, 144, 204
Find the greatest number which can divide 257 and 329 so as to leave a remainder 5 in each case.
Find the largest number that will divide 623, 729 and 841 leaving remainders 3, 9 and 1 respectively.