Question

HCF by prime factorization of 84 120 138​

Answer 1

84 = 2² × 3 × 7

120 = 2³ × 3 × 5

138 = 2 × 3 × 23

HCF = product of common terms with lowest power

HCF = 2 × 3 = 6

Answer 2

Answer:

Required HCF is 6.

Step-by-step explanation:

Here given numbers are 84,120,138.

Here we want to find HCF.

Now question is How can we find HCF?

HCF means Highest Common Factor.

By Some examples we can understand this concept easily.

Example -1:

Two numbers 9 and 18.

We are prime factorising of 9 and 18.

So,

$9 = 3 \times 3 \\ 18 = 2 \times 3 \times 3$

Here highest common factor is$3 \times 3 = 9$

So, HCF of 9 and 18 is 9.

Example -2:

Again we take two numbers 30 and 25.

We are prime factorising of 30 and 25.

So,

$30 = 2 \times 3 \times 5 \\ 25 = 5 \times 5$

Here highest common factor is $5$

So,HCF of 30 and 25 is 5.

Now given numbers are 84,120,138.

We are prime factorising of 84,120,138.

$84 = 2 \times 2 \times 3 \\ 120 = 2 \times 2 \times 2 \times 3 \ \\ 138 = 2 \times 2 \times 3 \times 23$

Here highest common factor is$2 \times 3 = 6$

Therefore required HCF is 6.