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The highest common factor of any two distinct prime numbers is:
0
3
1
2
1
Prime numbers have only two factors: 1 and themselves. Since they are distinct, they share no common factors other than 1. Therefore, their HCF is always 1.
Two distinct prime numbers.
HCF(p1тАЛ,p2тАЛ)=1┬аwhere┬аp1тАЛ,p2тАЛ┬аare┬аdistinct┬аprime┬аnumbers
Prime numbers have only two factors: 1 and themselves. Since they are distinct, they share no common factors other than 1. Therefore, their HCF is always 1.
Many students mistakenly think they have no common factor and select 0, but 1 is a factor of every integer.
Definition of Prime Numbers
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
pтИИPтЯ╣divisors(p)={1,p}
Identify Common Factors
For any two distinct prime numbers p1тАЛ and p2тАЛ, their sets of factors are 1,p1тАЛ and 1,p2тАЛ. The intersection of these sets is the set of common factors.
{1,p1тАЛ}тИй{1,p2тАЛ}={1}
Determine the Highest Common Factor (HCF)
The highest value in the set of common factors 1 is 1.
HCF(p1тАЛ,p2тАЛ)=1
C is correct because the only positive integer that divides any two distinct prime numbers is 1, thus their HCF is 1.
This concept is foundational for understanding the definition of 'relatively prime' (or coprime) numbers, where HCF(a,b)=1.
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