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What is the HCF of 2 prime numbers?
The highest common factor (HCF) of two numbers a and b is the highest possible number that divides the numbers a and b exactly, leaving the remainder 0.
Answer: HCF of 2 prime numbers is always 1.
Explanation:
Prime Numbers do not have any common factor apart from the universal factor this is 1. Numbers that have only 1 as their common factor are also known as co-prime numbers.
EXAMPLE 1: HCF OF 3 and 5
We consider 2 prime numbers 3 and 5.
HCF of 3 and 5 by Prime Factorization
3 = 1 × 3
5 = 1 × 5
The highest common factor among both is 1.
Hence, HCF is 1.
HCF of 3 and 5 by Long Division
- Step 1: Divide 5 by 3 and check the remainder.
- Step 2: Make the remainder 1 as the new divisor and the previous divisor 3 as the dividend and perform the long division again. The last divisor is our HCF.
- Step 3: Continue till you get the remainder as 0
Irrespective of the method used, HCF will always be 1.
EXAMPLE 2: HCF OF 2 and 5
We consider 2 prime numbers 2 and 5.
HCF of 2 and 5 by Prime Factorization
2 = 1 × 2
5 = 1 × 5
The highest common factor among both are 1
Hence, HCF is 1.
HCF of 2 and 5 by Long Division
- Step 1: Divide 5 by 2 and check the remainder.
- Step 2: Make the remainder 1 as the new divisor and the previous divisor 2 as the dividend and perform the long division again. The last divisor is our HCF.
- Step 3: Continue till you get the remainder as 0
So, we can conclude that the HCF of two prime numbers is 1.
Thus, the HCF of two prime numbers is always 1.
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