HCF of 120 and 75
HCF of 120 and 75 is the largest possible number that divides 120 and 75 exactly without any remainder. The factors of 120 and 75 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the HCF of 120 and 75 - prime factorization, Euclidean algorithm, and long division.
| 1. | HCF of 120 and 75 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 120 and 75?
Answer: HCF of 120 and 75 is 15.
Explanation:
The HCF of two non-zero integers, x(120) and y(75), is the highest positive integer m(15) that divides both x(120) and y(75) without any remainder.
Methods to Find HCF of 120 and 75
The methods to find the HCF of 120 and 75 are explained below.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
HCF of 120 and 75 by Listing Common Factors
- Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 75: 1, 3, 5, 15, 25, 75
There are 4 common factors of 120 and 75, that are 1, 3, 5, and 15. Therefore, the highest common factor of 120 and 75 is 15.
HCF of 120 and 75 by Prime Factorization
Prime factorization of 120 and 75 is (2 × 2 × 2 × 3 × 5) and (3 × 5 × 5) respectively. As visible, 120 and 75 have common prime factors. Hence, the HCF of 120 and 75 is 3 × 5 = 15.
HCF of 120 and 75 by Long Division
HCF of 120 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 120 (larger number) by 75 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (75) by the remainder (45).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (15) is the HCF of 120 and 75.
☛ Also Check:
- HCF of 60 and 72 = 12
- HCF of 1095 and 1168 = 73
- HCF of 40, 42 and 45 = 1
- HCF of 20 and 25 = 5
- HCF of 9 and 12 = 3
- HCF of 14 and 15 = 1
- HCF of 72, 108 and 180 = 36
FAQs on HCF of 120 and 75
What is the HCF of 120 and 75?
The HCF of 120 and 75 is 15. To calculate the Highest common factor of 120 and 75, we need to factor each number (factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the highest factor that exactly divides both 120 and 75, i.e., 15.
What are the Methods to Find HCF of 120 and 75?
There are three commonly used methods to find the HCF of 120 and 75.
- By Listing Common Factors
- By Prime Factorization
- By Long Division
What is the Relation Between LCM and HCF of 120, 75?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 120 and 75, i.e. HCF × LCM = 120 × 75.
How to Find the HCF of 120 and 75 by Long Division Method?
To find the HCF of 120, 75 using long division method, 120 is divided by 75. The corresponding divisor (15) when remainder equals 0 is taken as HCF.
How to Find the HCF of 120 and 75 by Prime Factorization?
To find the HCF of 120 and 75, we will find the prime factorization of the given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 75 = 3 × 5 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 120 and 75. Hence, HCF(120, 75) = 3 × 5 = 15
☛ Prime Number
If the HCF of 75 and 120 is 15, Find its LCM.
HCF(75, 120) × LCM(75, 120) = 75 × 120
Since the HCF of 75 and 120 = 15
⇒ 15 × LCM(75, 120) = 9000
Therefore, LCM = 600
☛ Highest Common Factor Calculator