Choose the correct answer
i) HCF of even no. and odd no. is even no.
ii) HCF of consecutive even no. and odd no. is other than one.
iii) both i) and ii) are true iv) both i) and ii) are not true
Answers
8=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.
Step-by-step explanation:
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.