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HCF of 777, 315 and 588
HCF of 777, 315 and 588 is the largest possible number that divides 777, 315 and 588 exactly without any remainder. The factors of 777, 315 and 588 are (1, 3, 7, 21, 37, 111, 259, 777), (1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315) and (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588) respectively. There are 3 commonly used methods to find the HCF of 777, 315 and 588  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 777, 315 and 588 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 777, 315 and 588?
Answer: HCF of 777, 315 and 588 is 21.
Explanation:
The HCF of three nonzero integers, x(777), y(315) and z(588), is the highest positive integer m(21) that divides x(777), y(315) and z(588) without any remainder.
Methods to Find HCF of 777, 315 and 588
The methods to find the HCF of 777, 315 and 588 are explained below.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
HCF of 777, 315 and 588 by Long Division
HCF of 777, 315 and 588 can be represented as HCF of (HCF of 777, 315) and 588. HCF(777, 315, 588) can be thus calculated by first finding HCF(777, 315) using long division and thereafter using this result with 588 to perform long division again.
 Step 1: Divide 777 (larger number) by 315 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (315) by the remainder (147). Repeat this process until the remainder = 0.
⇒ HCF(777, 315) = 21.  Step 3: Now to find the HCF of 21 and 588, we will perform a long division on 588 and 21.
 Step 4: For remainder = 0, divisor = 21 ⇒ HCF(21, 588) = 21
Thus, HCF(777, 315, 588) = HCF(HCF(777, 315), 588) = 21.
HCF of 777, 315 and 588 by Listing Common Factors
 Factors of 777: 1, 3, 7, 21, 37, 111, 259, 777
 Factors of 315: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
 Factors of 588: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
There are 4 common factors of 777, 315 and 588, that are 1, 3, 21, and 7. Therefore, the highest common factor of 777, 315 and 588 is 21.
HCF of 777, 315 and 588 by Prime Factorization
Prime factorization of 777, 315 and 588 is (3 × 7 × 37), (3 × 3 × 5 × 7) and (2 × 2 × 3 × 7 × 7) respectively. As visible, 777, 315 and 588 have common prime factors. Hence, the HCF of 777, 315 and 588 is 3 × 7 = 21.
☛ Also Check:
 HCF of 2 and 6 = 2
 HCF of 2, 3 and 4 = 1
 HCF of 35 and 40 = 5
 HCF of 16 and 27 = 1
 HCF of 120 and 144 = 24
 HCF of 12, 16 and 24 = 4
 HCF of 3 and 5 = 1
HCF of 777, 315 and 588 Examples

Example 1: Calculate the HCF of 777, 315, and 588 using LCM of the given numbers.
Solution:
Prime factorization of 777, 315 and 588 is given as,
 777 = 3 × 7 × 37
 315 = 3 × 3 × 5 × 7
 588 = 2 × 2 × 3 × 7 × 7
LCM(777, 315) = 11655, LCM(315, 588) = 8820, LCM(588, 777) = 21756, LCM(777, 315, 588) = 326340
⇒ HCF(777, 315, 588) = [(777 × 315 × 588) × LCM(777, 315, 588)]/[LCM(777, 315) × LCM (315, 588) × LCM(588, 777)]
⇒ HCF(777, 315, 588) = (143915940 × 326340)/(11655 × 8820 × 21756)
⇒ HCF(777, 315, 588) = 21.
Therefore, the HCF of 777, 315 and 588 is 21. 
Example 2: Find the highest number that divides 777, 315, and 588 completely.
Solution:
The highest number that divides 777, 315, and 588 exactly is their highest common factor.
 Factors of 777 = 1, 3, 7, 21, 37, 111, 259, 777
 Factors of 315 = 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
 Factors of 588 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The HCF of 777, 315, and 588 is 21.
∴ The highest number that divides 777, 315, and 588 is 21. 
Example 3: Verify the relation between the LCM and HCF of 777, 315 and 588.
Solution:
The relation between the LCM and HCF of 777, 315 and 588 is given as, HCF(777, 315, 588) = [(777 × 315 × 588) × LCM(777, 315, 588)]/[LCM(777, 315) × LCM (315, 588) × LCM(777, 588)]
⇒ Prime factorization of 777, 315 and 588: 777 = 3 × 7 × 37
 315 = 3 × 3 × 5 × 7
 588 = 2 × 2 × 3 × 7 × 7
∴ LCM of (777, 315), (315, 588), (777, 588), and (777, 315, 588) is 11655, 8820, 21756, and 326340 respectively.
Now, LHS = HCF(777, 315, 588) = 21.
And, RHS = [(777 × 315 × 588) × LCM(777, 315, 588)]/[LCM(777, 315) × LCM (315, 588) × LCM(777, 588)] = [(143915940) × 326340]/[11655 × 8820 × 21756]
LHS = RHS = 21.
Hence verified.
FAQs on HCF of 777, 315 and 588
What is the HCF of 777, 315 and 588?
The HCF of 777, 315 and 588 is 21. To calculate the highest common factor (HCF) of 777, 315 and 588, we need to factor each number (factors of 777 = 1, 3, 7, 21, 37, 111, 259, 777; factors of 315 = 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315; factors of 588 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588) and choose the highest factor that exactly divides 777, 315 and 588, i.e., 21.
How to Find the HCF of 777, 315 and 588 by Prime Factorization?
To find the HCF of 777, 315 and 588, we will find the prime factorization of given numbers, i.e. 777 = 3 × 7 × 37; 315 = 3 × 3 × 5 × 7; 588 = 2 × 2 × 3 × 7 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 777, 315 and 588. Hence, HCF(777, 315, 588) = 3 × 7 = 21
☛ Prime Number
Which of the following is HCF of 777, 315 and 588? 21, 789, 826, 820, 817, 786, 793, 784, 796
HCF of 777, 315, 588 will be the number that divides 777, 315, and 588 without leaving any remainder. The only number that satisfies the given condition is 21.
What is the Relation Between LCM and HCF of 777, 315 and 588?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 777, 315 and 588, i.e. HCF(777, 315, 588) = [(777 × 315 × 588) × LCM(777, 315, 588)]/[LCM(777, 315) × LCM (315, 588) × LCM(777, 588)].
☛ HCF Calculator
What are the Methods to Find HCF of 777, 315 and 588?
There are three commonly used methods to find the HCF of 777, 315 and 588.
 By Long Division
 By Prime Factorization
 By Euclidean Algorithm
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