HCF of 1152 and 1664
HCF of 1152 and 1664 is the largest possible number that divides 1152 and 1664 exactly without any remainder. The factors of 1152 and 1664 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152 and 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 respectively. There are 3 commonly used methods to find the HCF of 1152 and 1664 - prime factorization, long division, and Euclidean algorithm.
| 1. | HCF of 1152 and 1664 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 1152 and 1664?
Answer: HCF of 1152 and 1664 is 128.
Explanation:
The HCF of two non-zero integers, x(1152) and y(1664), is the highest positive integer m(128) that divides both x(1152) and y(1664) without any remainder.
Methods to Find HCF of 1152 and 1664
Let's look at the different methods for finding the HCF of 1152 and 1664.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
HCF of 1152 and 1664 by Listing Common Factors
- Factors of 1152: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152
- Factors of 1664: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664
There are 8 common factors of 1152 and 1664, that are 32, 1, 2, 64, 4, 128, 8, and 16. Therefore, the highest common factor of 1152 and 1664 is 128.
HCF of 1152 and 1664 by Prime Factorization
Prime factorization of 1152 and 1664 is (2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 2 × 2 × 2 × 13) respectively. As visible, 1152 and 1664 have common prime factors. Hence, the HCF of 1152 and 1664 is 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128.
HCF of 1152 and 1664 by Long Division
HCF of 1152 and 1664 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 1664 (larger number) by 1152 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (1152) by the remainder (512).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (128) is the HCF of 1152 and 1664.
☛ Also Check:
- HCF of 10 and 15 = 5
- HCF of 3 and 9 = 3
- HCF of 7 and 9 = 1
- HCF of 441, 567 and 693 = 63
- HCF of 12 and 16 = 4
- HCF of 27 and 36 = 9
- HCF of 24 and 36 = 12
FAQs on HCF of 1152 and 1664
What is the HCF of 1152 and 1664?
The HCF of 1152 and 1664 is 128. To calculate the HCF of 1152 and 1664, we need to factor each number (factors of 1152 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152; factors of 1664 = 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664) and choose the highest factor that exactly divides both 1152 and 1664, i.e., 128.
How to Find the HCF of 1152 and 1664 by Long Division Method?
To find the HCF of 1152, 1664 using long division method, 1664 is divided by 1152. The corresponding divisor (128) when remainder equals 0 is taken as HCF.
How to Find the HCF of 1152 and 1664 by Prime Factorization?
To find the HCF of 1152 and 1664, we will find the prime factorization of the given numbers, i.e. 1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3; 1664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13.
⇒ Since 2, 2, 2, 2, 2, 2, 2 are common terms in the prime factorization of 1152 and 1664. Hence, HCF(1152, 1664) = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
☛ Prime Number
What is the Relation Between LCM and HCF of 1152, 1664?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 1152 and 1664, i.e. HCF × LCM = 1152 × 1664.
What are the Methods to Find HCF of 1152 and 1664?
There are three commonly used methods to find the HCF of 1152 and 1664.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
If the HCF of 1664 and 1152 is 128, Find its LCM.
HCF(1664, 1152) × LCM(1664, 1152) = 1664 × 1152
Since the HCF of 1664 and 1152 = 128
⇒ 128 × LCM(1664, 1152) = 1916928
Therefore, LCM = 14976
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