GCF of 35, 56 and 63
GCF of 35, 56 and 63 is the largest possible number that divides 35, 56 and 63 exactly without any remainder. The factors of 35, 56 and 63 are (1, 5, 7, 35), (1, 2, 4, 7, 8, 14, 28, 56) and (1, 3, 7, 9, 21, 63) respectively. There are 3 commonly used methods to find the GCF of 35, 56 and 63  long division, prime factorization, and Euclidean algorithm.
1.  GCF of 35, 56 and 63 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 35, 56 and 63?
Answer: GCF of 35, 56 and 63 is 7.
Explanation:
The GCF of three nonzero integers, x(35), y(56) and z(63), is the greatest positive integer m(7) that divides x(35), y(56) and z(63) without any remainder.
Methods to Find GCF of 35, 56 and 63
Let's look at the different methods for finding the GCF of 35, 56 and 63.
 Prime Factorization Method
 Long Division Method
 Listing Common Factors
GCF of 35, 56 and 63 by Prime Factorization
Prime factorization of 35, 56 and 63 is (5 × 7), (2 × 2 × 2 × 7) and (3 × 3 × 7) respectively. As visible, 35, 56 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 35, 56 and 63 is 7.
GCF of 35, 56 and 63 by Long Division
GCF of 35, 56 and 63 can be represented as GCF of (GCF of 35, 56) and 63. GCF(35, 56, 63) can be thus calculated by first finding GCF(35, 56) using long division and thereafter using this result with 63 to perform long division again.
 Step 1: Divide 56 (larger number) by 35 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (21). Repeat this process until the remainder = 0.
⇒ GCF(35, 56) = 7.  Step 3: Now to find the GCF of 7 and 63, we will perform a long division on 63 and 7.
 Step 4: For remainder = 0, divisor = 7 ⇒ GCF(7, 63) = 7
Thus, GCF(35, 56, 63) = GCF(GCF(35, 56), 63) = 7.
GCF of 35, 56 and 63 by Listing Common Factors
 Factors of 35: 1, 5, 7, 35
 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 63: 1, 3, 7, 9, 21, 63
There are 2 common factors of 35, 56 and 63, that are 1 and 7. Therefore, the greatest common factor of 35, 56 and 63 is 7.
☛ Also Check:
 GCF of 10 and 20 = 10
 GCF of 9 and 15 = 3
 GCF of 4 and 7 = 1
 GCF of 75, 8 and 21 = 1
 GCF of 64 and 96 = 32
 GCF of 48 and 60 = 12
 GCF of 28 and 49 = 7
GCF of 35, 56 and 63 Examples

Example 1: Calculate the GCF of 35, 56, and 63 using LCM of the given numbers.
Solution:
Prime factorization of 35, 56 and 63 is given as,
 35 = 5 × 7
 56 = 2 × 2 × 2 × 7
 63 = 3 × 3 × 7
LCM(35, 56) = 280, LCM(56, 63) = 504, LCM(63, 35) = 315, LCM(35, 56, 63) = 2520
⇒ GCF(35, 56, 63) = [(35 × 56 × 63) × LCM(35, 56, 63)]/[LCM(35, 56) × LCM (56, 63) × LCM(63, 35)]
⇒ GCF(35, 56, 63) = (123480 × 2520)/(280 × 504 × 315)
⇒ GCF(35, 56, 63) = 7.
Therefore, the GCF of 35, 56 and 63 is 7. 
Example 2: Find the greatest number that divides 35, 56, and 63 completely.
Solution:
The greatest number that divides 35, 56, and 63 exactly is their greatest common factor.
 Factors of 35 = 1, 5, 7, 35
 Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 63 = 1, 3, 7, 9, 21, 63
The GCF of 35, 56, and 63 is 7.
∴ The greatest number that divides 35, 56, and 63 is 7. 
Example 3: Verify the relation between the LCM and GCF of 35, 56 and 63.
Solution:
The relation between the LCM and GCF of 35, 56 and 63 is given as, GCF(35, 56, 63) = [(35 × 56 × 63) × LCM(35, 56, 63)]/[LCM(35, 56) × LCM (56, 63) × LCM(35, 63)]
⇒ Prime factorization of 35, 56 and 63: 35 = 5 × 7
 56 = 2 × 2 × 2 × 7
 63 = 3 × 3 × 7
∴ LCM of (35, 56), (56, 63), (35, 63), and (35, 56, 63) is 280, 504, 315, and 2520 respectively.
Now, LHS = GCF(35, 56, 63) = 7.
And, RHS = [(35 × 56 × 63) × LCM(35, 56, 63)]/[LCM(35, 56) × LCM (56, 63) × LCM(35, 63)] = [(123480) × 2520]/[280 × 504 × 315]
LHS = RHS = 7.
Hence verified.
FAQs on GCF of 35, 56 and 63
What is the GCF of 35, 56 and 63?
The GCF of 35, 56 and 63 is 7. To calculate the greatest common factor of 35, 56 and 63, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides 35, 56 and 63, i.e., 7.
What is the Relation Between LCM and GCF of 35, 56 and 63?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 35, 56 and 63, i.e. GCF(35, 56, 63) = [(35 × 56 × 63) × LCM(35, 56, 63)]/[LCM(35, 56) × LCM (56, 63) × LCM(35, 63)].
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 35, 56 and 63?
There are three commonly used methods to find the GCF of 35, 56 and 63.
 By Prime Factorization
 By Listing Common Factors
 By Long Division
Which of the following is GCF of 35, 56 and 63? 7, 68, 101, 80, 92, 100, 107, 94
GCF of 35, 56, 63 will be the number that divides 35, 56, and 63 without leaving any remainder. The only number that satisfies the given condition is 7.
How to Find the GCF of 35, 56 and 63 by Prime Factorization?
To find the GCF of 35, 56 and 63, we will find the prime factorization of given numbers, i.e. 35 = 5 × 7; 56 = 2 × 2 × 2 × 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 35, 56 and 63. Hence, GCF(35, 56, 63) = 7.
☛ What is a Prime Number?
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