Question

plzz help me....someone

Answer 1

Answer:

a) HCF of any two consecutive natural numbers is 1. because the difference between two consecutive numbers is one & if the HCF is greater than one the the two consecutive numbers has to be divisible by that number which is not possible

b) 2 is the H.C.F for numbers 4 and 6 because 2 is the only common prime factor for both 4 and 6. 2 is the H.C.F for numbers 10 and 12 because 2 is the only common prime factor for both 10 and 12. 1 is the H.CF of two consecutive odd numbers.

c)The number 2 does not divide them because they are odd. If any integer larger than 2 divides the smaller it gives a remainder of 2 when divided into the larger, and so is not a common divisor. Hence: the largest integer that divides them both (HCF) is 1.

d) A prime number is the number which has only 2 factors-1 and the number itself.Hence 1 is the only common factor for 2 prime numbers making it HCF.