HCF of 960 and 432
HCF of 960 and 432 is the largest possible number that divides 960 and 432 exactly without any remainder. The factors of 960 and 432 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432 respectively. There are 3 commonly used methods to find the HCF of 960 and 432  long division, prime factorization, and Euclidean algorithm.
1.  HCF of 960 and 432 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 960 and 432?
Answer: HCF of 960 and 432 is 48.
Explanation:
The HCF of two nonzero integers, x(960) and y(432), is the highest positive integer m(48) that divides both x(960) and y(432) without any remainder.
Methods to Find HCF of 960 and 432
Let's look at the different methods for finding the HCF of 960 and 432.
 Long Division Method
 Prime Factorization Method
 Listing Common Factors
HCF of 960 and 432 by Long Division
HCF of 960 and 432 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 960 (larger number) by 432 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (432) by the remainder (96).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (48) is the HCF of 960 and 432.
HCF of 960 and 432 by Prime Factorization
Prime factorization of 960 and 432 is (2 × 2 × 2 × 2 × 2 × 2 × 3 × 5) and (2 × 2 × 2 × 2 × 3 × 3 × 3) respectively. As visible, 960 and 432 have common prime factors. Hence, the HCF of 960 and 432 is 2 × 2 × 2 × 2 × 3 = 48.
HCF of 960 and 432 by Listing Common Factors
 Factors of 960: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
 Factors of 432: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
There are 10 common factors of 960 and 432, that are 1, 2, 3, 4, 6, 8, 12, 16, 48, and 24. Therefore, the highest common factor of 960 and 432 is 48.
☛ Also Check:
 HCF of 336, 240 and 96 = 48
 HCF of 7 and 11 = 1
 HCF of 120 and 150 = 30
 HCF of 0 and 6 = 6
 HCF of 12, 15 and 18 = 3
 HCF of 2 and 6 = 2
 HCF of 1651 and 2032 = 127
HCF of 960 and 432 Examples

Example 1: For two numbers, HCF = 48 and LCM = 8640. If one number is 432, find the other number.
Solution:
Given: HCF (z, 432) = 48 and LCM (z, 432) = 8640
∵ HCF × LCM = 432 × (z)
⇒ z = (HCF × LCM)/432
⇒ z = (48 × 8640)/432
⇒ z = 960
Therefore, the other number is 960. 
Example 2: Find the highest number that divides 960 and 432 exactly.
Solution:
The highest number that divides 960 and 432 exactly is their highest common factor, i.e. HCF of 960 and 432.
⇒ Factors of 960 and 432: Factors of 960 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
 Factors of 432 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
Therefore, the HCF of 960 and 432 is 48.

Example 3: The product of two numbers is 414720. If their HCF is 48, what is their LCM?
Solution:
Given: HCF = 48 and product of numbers = 414720
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 414720/48
Therefore, the LCM is 8640.
FAQs on HCF of 960 and 432
What is the HCF of 960 and 432?
The HCF of 960 and 432 is 48. To calculate the HCF of 960 and 432, we need to factor each number (factors of 960 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960; factors of 432 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432) and choose the highest factor that exactly divides both 960 and 432, i.e., 48.
What is the Relation Between LCM and HCF of 960, 432?
The following equation can be used to express the relation between LCM and HCF of 960 and 432, i.e. HCF × LCM = 960 × 432.
How to Find the HCF of 960 and 432 by Long Division Method?
To find the HCF of 960, 432 using long division method, 960 is divided by 432. The corresponding divisor (48) when remainder equals 0 is taken as HCF.
If the HCF of 432 and 960 is 48, Find its LCM.
HCF(432, 960) × LCM(432, 960) = 432 × 960
Since the HCF of 432 and 960 = 48
⇒ 48 × LCM(432, 960) = 414720
Therefore, LCM = 8640
☛ HCF Calculator
How to Find the HCF of 960 and 432 by Prime Factorization?
To find the HCF of 960 and 432, we will find the prime factorization of the given numbers, i.e. 960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5; 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3.
⇒ Since 2, 2, 2, 2, 3 are common terms in the prime factorization of 960 and 432. Hence, HCF(960, 432) = 2 × 2 × 2 × 2 × 3 = 48
☛ Prime Number
What are the Methods to Find HCF of 960 and 432?
There are three commonly used methods to find the HCF of 960 and 432.
 By Listing Common Factors
 By Prime Factorization
 By Long Division
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