find the HCF of 34 and 78 using prime factorise method????
Answers
Answer:
The HCF of 34 and 78 can be obtained like this:
The factors of 34 are 34, 17, 2, 1.
The factors of 78 are 78, 39, 26, 13, 6, 3, 2, 1.
The common factors of 34 and 78 are 2, 1, intersecting the two sets above.
In the intersection factors of 34 ∩ factors of 78 the greatest element is 2.
Therefore, the greatest common factor of 34 and 78 is 2.
Taking the above into account you also know how to find all the common factors of 34 and 78, not just the greatest. In the next section we show you how to calculate the gcf of thirty-four and seventy-eight by means of two more methods.
How to find the GCF of 34 and 78
The greatest common factor of 34 and 78 can be computed by using the least common multiple aka lcm of 34 and 78. This is the easiest approach:
gcf (34,78) =
34
×
78
l
c
m
(
34
,
78
)
=
2652
1326
= 2
Alternatively, the gcf of 34 and 78 can be found using the prime factorization of 34 and 78:
The prime factorization of 34 is: 2 x 17
The prime factorization of 78 is: 2 x 3 x 13
The prime factors and multiplicities 34 and 78 have in common are: 2
2 is the gcf of 34 and 78
gcf(34,78) = 2
In any case, the easiest way to compute the gcf of two numbers like 34 and 78 is by using our calculator below. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 34,78. The calculation is conducted automatically.