HCF of 306 and 657
HCF of 306 and 657 is the largest possible number that divides 306 and 657 exactly without any remainder. The factors of 306 and 657 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306 and 1, 3, 9, 73, 219, 657 respectively. There are 3 commonly used methods to find the HCF of 306 and 657  Euclidean algorithm, long division, and prime factorization.
1.  HCF of 306 and 657 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 306 and 657?
Answer: HCF of 306 and 657 is 9.
Explanation:
The HCF of two nonzero integers, x(306) and y(657), is the highest positive integer m(9) that divides both x(306) and y(657) without any remainder.
Methods to Find HCF of 306 and 657
The methods to find the HCF of 306 and 657 are explained below.
 Prime Factorization Method
 Listing Common Factors
 Long Division Method
HCF of 306 and 657 by Prime Factorization
Prime factorization of 306 and 657 is (2 × 3 × 3 × 17) and (3 × 3 × 73) respectively. As visible, 306 and 657 have common prime factors. Hence, the HCF of 306 and 657 is 3 × 3 = 9.
HCF of 306 and 657 by Listing Common Factors
 Factors of 306: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
 Factors of 657: 1, 3, 9, 73, 219, 657
There are 3 common factors of 306 and 657, that are 1, 3, and 9. Therefore, the highest common factor of 306 and 657 is 9.
HCF of 306 and 657 by Long Division
HCF of 306 and 657 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 657 (larger number) by 306 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (306) by the remainder (45).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the HCF of 306 and 657.
☛ Also Check:
 HCF of 12, 16 and 24 = 4
 HCF of 27 and 36 = 9
 HCF of 15, 25 and 30 = 5
 HCF of 513, 1134 and 1215 = 27
 HCF of 15 and 20 = 5
 HCF of 1517 and 902 = 41
 HCF of 6, 72 and 120 = 6
HCF of 306 and 657 Examples

Example 1: For two numbers, HCF = 9 and LCM = 22338. If one number is 657, find the other number.
Solution:
Given: HCF (y, 657) = 9 and LCM (y, 657) = 22338
∵ HCF × LCM = 657 × (y)
⇒ y = (HCF × LCM)/657
⇒ y = (9 × 22338)/657
⇒ y = 306
Therefore, the other number is 306. 
Example 2: The product of two numbers is 201042. If their HCF is 9, what is their LCM?
Solution:
Given: HCF = 9 and product of numbers = 201042
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 201042/9
Therefore, the LCM is 22338. 
Example 3: Find the highest number that divides 306 and 657 exactly.
Solution:
The highest number that divides 306 and 657 exactly is their highest common factor, i.e. HCF of 306 and 657.
⇒ Factors of 306 and 657: Factors of 306 = 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
 Factors of 657 = 1, 3, 9, 73, 219, 657
Therefore, the HCF of 306 and 657 is 9.
FAQs on HCF of 306 and 657
What is the HCF of 306 and 657?
The HCF of 306 and 657 is 9. To calculate the Highest common factor of 306 and 657, we need to factor each number (factors of 306 = 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306; factors of 657 = 1, 3, 9, 73, 219, 657) and choose the highest factor that exactly divides both 306 and 657, i.e., 9.
What is the Relation Between LCM and HCF of 306, 657?
The following equation can be used to express the relation between LCM and HCF of 306 and 657, i.e. HCF × LCM = 306 × 657.
What are the Methods to Find HCF of 306 and 657?
There are three commonly used methods to find the HCF of 306 and 657.
 By Listing Common Factors
 By Long Division
 By Prime Factorization
If the HCF of 657 and 306 is 9, Find its LCM.
HCF(657, 306) × LCM(657, 306) = 657 × 306
Since the HCF of 657 and 306 = 9
⇒ 9 × LCM(657, 306) = 201042
Therefore, LCM = 22338
☛ HCF Calculator
How to Find the HCF of 306 and 657 by Prime Factorization?
To find the HCF of 306 and 657, we will find the prime factorization of the given numbers, i.e. 306 = 2 × 3 × 3 × 17; 657 = 3 × 3 × 73.
⇒ Since 3, 3 are common terms in the prime factorization of 306 and 657. Hence, HCF(306, 657) = 3 × 3 = 9
☛ Prime Number
How to Find the HCF of 306 and 657 by Long Division Method?
To find the HCF of 306, 657 using long division method, 657 is divided by 306. The corresponding divisor (9) when remainder equals 0 is taken as HCF.
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