12 18 20 h.c.f solve
Answers
Question:-
what is the HCF of 12, 18, and 20.
Answer:-
let us represent each number as product of prime factors
12 can be written as 2 × 2 × 3
18 can be written as 2 × 3 × 3
20 can be written as 2 × 2 × 5
we can see that only 2 is common to all the numbers so 2 is the highest common factor of 12, 18, 20.
Answer:
What is HCF of 12 and 18?
Answer: HCF of 12 and 18 is 6.
HCF of 12 and 18
Explanation:
The HCF of two non-zero integers, x(12) and y(18), is the highest positive integer m(6) that divides both x(12) and y(18) without any remainder.
Methods to Find HCF of 12 and 18
Let's look at the different methods for finding the HCF of 12 and 18.
Prime Factorization Method
Long Division Method
Listing Common Factors
HCF of 12 and 18 by Prime Factorization
HCF of 12 and 18 by Prime Factorization
Prime factorization of 12 and 18 is (2 × 2 × 3) and (2 × 3 × 3) respectively. As visible, 12 and 18 have common prime factors. Hence, the HCF of 12 and 18 is 2 × 3 = 6.
HCF of 12 and 18 by Long Division
HCF of 12 and 18 by Long Division
HCF of 12 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
Step 1: Divide 18 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the HCF of 12 and 18.
HCF of 12 and 18 by Listing Common Factors
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
There are 4 common factors of 12 and 18, that are 1, 2, 3, and 6. Therefore, the highest common factor of 12 and 18 is 6.
☛ Also Check:
HCF of 60 and 72 = 12
HCF of 18 and 24 = 6
HCF of 4 and 8 = 4
HCF of 609 and 957 = 87
HCF of 145 and 232 = 29
HCF of 6 and 20 = 2
HCF of 144, 180 and 192 = 12
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HCF of 12 and 18 Examples
Example 1: For two numbers, HCF = 6 and LCM = 36. If one number is 12, find the other number.
,
Solution:
Given: HCF (y, 12) = 6 and LCM (y, 12) = 36
∵ HCF × LCM = 12 × (y)
⇒ y = (HCF × LCM)/12
⇒ y = (6 × 36)/12
⇒ y = 18
Therefore, the other number is 18.
Example 2: Find the highest number that divides 12 and 18 exactly.
Solution:
The highest number that divides 12 and 18 exactly is their highest common factor, i.e. HCF of 12 and 18.
⇒ Factors of 12 and 18:
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the HCF of 12 and 18 is 6.
Example 3: Find the HCF of 12 and 18, if their LCM is 36.
Solution:
∵ LCM × HCF = 12 × 18
⇒ HCF(12, 18) = (12 × 18)/36 = 6
Therefore, the highest common