Solved Example on HCF of 36 and 84
Example 1: What is the HCF of 36 and 84 if their LCM is 252?
Solution:
We know, LCM × HCF = product of numbers
HCF = Product of two numbers/LCM
HCF = 36 × 84/252
HCF = 3024/252
Therefore, the HCF(36, 84) is 12.
Example 2: Find the highest number that divides 36 and 18 exactly.
Solution:
Prime factor of 36 and 18, respectively, are,
36 = 2 × 2 × 3 × 3
18 = 2 × 3 × 3
Common prime factors of 36 and 18 are: 2, 3, 3
Hence, HCF(36,18) = 2 × 3 × 3= 18
Example 3: For two numbers, HCF = 20 and LCM = 250. If one number is 25, find the other number.
Solution:
Let the other number be x
We know, LCM × HCF = product of numbers
Hence,
20 × 250 = 25 × x
⇒ x = (20 × 250)/25
⇒ x = (5000)/25
⇒ x = 200
HCF of 36 and 84
HCF of 36 and 84 is 12. HCF or Highest Common Factor is the greatest number that divides two or more numbers. HCF is also known as Greatest Common Measure (GCM) or Greatest Common Divisor (GCD).
In this article, we will learn about how to find HCF of 36 and 84, what is HCF, finding HCF by prime factorization method, listing common factor and by long division method, HCF vs LCM of 36 and 84 along with some solved examples, and practice problems.