HCF of 294, 252 and 210
HCF of 294, 252 and 210 is the largest possible number that divides 294, 252 and 210 exactly without any remainder. The factors of 294, 252 and 210 are (1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294), (1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252) and (1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210) respectively. There are 3 commonly used methods to find the HCF of 294, 252 and 210  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 294, 252 and 210 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 294, 252 and 210?
Answer: HCF of 294, 252 and 210 is 42.
Explanation:
The HCF of three nonzero integers, x(294), y(252) and z(210), is the highest positive integer m(42) that divides x(294), y(252) and z(210) without any remainder.
Methods to Find HCF of 294, 252 and 210
Let's look at the different methods for finding the HCF of 294, 252 and 210.
 Listing Common Factors
 Prime Factorization Method
 Long Division Method
HCF of 294, 252 and 210 by Listing Common Factors
 Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
 Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
 Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
There are 8 common factors of 294, 252 and 210, that are 1, 2, 3, 6, 7, 42, 14, and 21. Therefore, the highest common factor of 294, 252 and 210 is 42.
HCF of 294, 252 and 210 by Prime Factorization
Prime factorization of 294, 252 and 210 is (2 × 3 × 7 × 7), (2 × 2 × 3 × 3 × 7) and (2 × 3 × 5 × 7) respectively. As visible, 294, 252 and 210 have common prime factors. Hence, the HCF of 294, 252 and 210 is 2 × 3 × 7 = 42.
HCF of 294, 252 and 210 by Long Division
HCF of 294, 252 and 210 can be represented as HCF of (HCF of 294, 252) and 210. HCF(294, 252, 210) can be thus calculated by first finding HCF(294, 252) using long division and thereafter using this result with 210 to perform long division again.
 Step 1: Divide 294 (larger number) by 252 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (252) by the remainder (42). Repeat this process until the remainder = 0.
⇒ HCF(294, 252) = 42.  Step 3: Now to find the HCF of 42 and 210, we will perform a long division on 210 and 42.
 Step 4: For remainder = 0, divisor = 42 ⇒ HCF(42, 210) = 42
Thus, HCF(294, 252, 210) = HCF(HCF(294, 252), 210) = 42.
☛ Also Check:
 HCF of 4 and 12 = 4
 HCF of 513, 1134 and 1215 = 27
 HCF of 95 and 152 = 19
 HCF of 4 and 9 = 1
 HCF of 72 and 120 = 24
 HCF of 408 and 1032 = 24
 HCF of 2048 and 960 = 64
HCF of 294, 252 and 210 Examples

Example 1: Calculate the HCF of 294, 252, and 210 using LCM of the given numbers.
Solution:
Prime factorization of 294, 252 and 210 is given as,
 294 = 2 × 3 × 7 × 7
 252 = 2 × 2 × 3 × 3 × 7
 210 = 2 × 3 × 5 × 7
LCM(294, 252) = 1764, LCM(252, 210) = 1260, LCM(210, 294) = 1470, LCM(294, 252, 210) = 8820
⇒ HCF(294, 252, 210) = [(294 × 252 × 210) × LCM(294, 252, 210)]/[LCM(294, 252) × LCM (252, 210) × LCM(210, 294)]
⇒ HCF(294, 252, 210) = (15558480 × 8820)/(1764 × 1260 × 1470)
⇒ HCF(294, 252, 210) = 42.
Therefore, the HCF of 294, 252 and 210 is 42. 
Example 2: Verify the relation between the LCM and HCF of 294, 252 and 210.
Solution:
The relation between the LCM and HCF of 294, 252 and 210 is given as, HCF(294, 252, 210) = [(294 × 252 × 210) × LCM(294, 252, 210)]/[LCM(294, 252) × LCM (252, 210) × LCM(294, 210)]
⇒ Prime factorization of 294, 252 and 210: 294 = 2 × 3 × 7 × 7
 252 = 2 × 2 × 3 × 3 × 7
 210 = 2 × 3 × 5 × 7
∴ LCM of (294, 252), (252, 210), (294, 210), and (294, 252, 210) is 1764, 1260, 1470, and 8820 respectively.
Now, LHS = HCF(294, 252, 210) = 42.
And, RHS = [(294 × 252 × 210) × LCM(294, 252, 210)]/[LCM(294, 252) × LCM (252, 210) × LCM(294, 210)] = [(15558480) × 8820]/[1764 × 1260 × 1470]
LHS = RHS = 42.
Hence verified. 
Example 3: Find the highest number that divides 294, 252, and 210 completely.
Solution:
The highest number that divides 294, 252, and 210 exactly is their highest common factor.
 Factors of 294 = 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
 Factors of 252 = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
 Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 294, 252, and 210 is 42.
∴ The highest number that divides 294, 252, and 210 is 42.
FAQs on HCF of 294, 252 and 210
What is the HCF of 294, 252 and 210?
The HCF of 294, 252 and 210 is 42. To calculate the highest common factor of 294, 252 and 210, we need to factor each number (factors of 294 = 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294; factors of 252 = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252; factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210) and choose the highest factor that exactly divides 294, 252 and 210, i.e., 42.
How to Find the HCF of 294, 252 and 210 by Prime Factorization?
To find the HCF of 294, 252 and 210, we will find the prime factorization of given numbers, i.e. 294 = 2 × 3 × 7 × 7; 252 = 2 × 2 × 3 × 3 × 7; 210 = 2 × 3 × 5 × 7.
⇒ Since 2, 3, 7 are common terms in the prime factorization of 294, 252 and 210. Hence, HCF(294, 252, 210) = 2 × 3 × 7 = 42
☛ What is a Prime Number?
Which of the following is HCF of 294, 252 and 210? 42, 307, 307, 320, 311, 340
HCF of 294, 252, 210 will be the number that divides 294, 252, and 210 without leaving any remainder. The only number that satisfies the given condition is 42.
What is the Relation Between LCM and HCF of 294, 252 and 210?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 294, 252 and 210, i.e. HCF(294, 252, 210) = [(294 × 252 × 210) × LCM(294, 252, 210)]/[LCM(294, 252) × LCM (252, 210) × LCM(294, 210)].
☛ HCF Calculator
What are the Methods to Find HCF of 294, 252 and 210?
There are three commonly used methods to find the HCF of 294, 252 and 210.
 By Long Division
 By Euclidean Algorithm
 By Prime Factorization
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