Question

What is the HCF of two consecutive? (3)

a.) Natural numbers

b.) Even numbers

c.) Odd numbers​

Answer 1

What is the HCF of two consecutive

(i) numbers? (ii) even numbers? (iii) odd numbers?

SOLUTION:

i) Let the consecutive numbers be 8 and 9.

8=2\times2\times28=2×2×2

9=3\times39=3×3

common factor of 8 and 9 =1

thus, HCF of 8 and 9 is 1.

therefore, HCF of two consecutive number is 1.

ii) let the two consecutive numbers be 10 and 12

10=2\times510=2×5

12=2\times2\times312=2×2×3

common factor of 10 and 12 is 2

HCF of 10 and 12 is 2.

hence, the HCF of two consecutive even numbers is 2.

iii) let the two consecutive odd numbers be 3 and 5.

3=1\times33=1×3

5=1\times55=1×5

common factor between 3 and 5 is 1

thus HCF of 3 and 5 is1

hence, the HCF of two consecutive odd number is 1.