HCF of 52 and 117
HCF of 52 and 117 is the largest possible number that divides 52 and 117 exactly without any remainder. The factors of 52 and 117 are 1, 2, 4, 13, 26, 52 and 1, 3, 9, 13, 39, 117 respectively. There are 3 commonly used methods to find the HCF of 52 and 117 - long division, prime factorization, and Euclidean algorithm.
| 1. | HCF of 52 and 117 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 52 and 117?
Answer: HCF of 52 and 117 is 13.
Explanation:
The HCF of two non-zero integers, x(52) and y(117), is the highest positive integer m(13) that divides both x(52) and y(117) without any remainder.
Methods to Find HCF of 52 and 117
Let's look at the different methods for finding the HCF of 52 and 117.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
HCF of 52 and 117 by Long Division
HCF of 52 and 117 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 117 (larger number) by 52 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (52) by the remainder (13).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (13) is the HCF of 52 and 117.
HCF of 52 and 117 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 117 and Y = 52
- HCF(117, 52) = HCF(52, 117 mod 52) = HCF(52, 13)
- HCF(52, 13) = HCF(13, 52 mod 13) = HCF(13, 0)
- HCF(13, 0) = 13 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 52 and 117 is 13.
HCF of 52 and 117 by Prime Factorization
Prime factorization of 52 and 117 is (2 × 2 × 13) and (3 × 3 × 13) respectively. As visible, 52 and 117 have only one common prime factor i.e. 13. Hence, the HCF of 52 and 117 is 13.
☛ Also Check:
- HCF of 4 and 5 = 1
- HCF of 120 and 150 = 30
- HCF of 17, 23 and 29 = 1
- HCF of 24 and 36 = 12
- HCF of 64 and 72 = 8
- HCF of 867 and 255 = 51
- HCF of 68 and 119 = 17
FAQs on HCF of 52 and 117
What is the HCF of 52 and 117?
The HCF of 52 and 117 is 13. To calculate the Highest common factor of 52 and 117, we need to factor each number (factors of 52 = 1, 2, 4, 13, 26, 52; factors of 117 = 1, 3, 9, 13, 39, 117) and choose the highest factor that exactly divides both 52 and 117, i.e., 13.
How to Find the HCF of 52 and 117 by Long Division Method?
To find the HCF of 52, 117 using long division method, 117 is divided by 52. The corresponding divisor (13) when remainder equals 0 is taken as HCF.
What is the Relation Between LCM and HCF of 52, 117?
The following equation can be used to express the relation between LCM and HCF of 52 and 117, i.e. HCF × LCM = 52 × 117.
How to Find the HCF of 52 and 117 by Prime Factorization?
To find the HCF of 52 and 117, we will find the prime factorization of the given numbers, i.e. 52 = 2 × 2 × 13; 117 = 3 × 3 × 13.
⇒ Since 13 is the only common prime factor of 52 and 117. Hence, HCF (52, 117) = 13.
☛ Prime Numbers
What are the Methods to Find HCF of 52 and 117?
There are three commonly used methods to find the HCF of 52 and 117.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
If the HCF of 117 and 52 is 13, Find its LCM.
HCF(117, 52) × LCM(117, 52) = 117 × 52
Since the HCF of 117 and 52 = 13
⇒ 13 × LCM(117, 52) = 6084
Therefore, LCM = 468
☛ HCF Calculator