GCF of 15 and 64
GCF of 15 and 64 is the largest possible number that divides 15 and 64 exactly without any residual. The factors of 15 and 64 are 1, iii, 5, 15 and 1, two, 4, 8, sixteen, 32, 64 respectively. At that place are 3 normally used methods to find the GCF of 15 and 64 – long division, Euclidean algorithm, and prime factorization.
1.  GCF of 15 and 64 
two.  Listing of Methods 
3.  Solved Examples 
iv.  FAQs 
What is GCF of xv and 64?
Reply:
GCF of 15 and 64 is i.
Explanation:
The GCF of two nonzero integers, x(15) and y(64), is the greatest positive integer m(ane) that divides both x(15) and y(64) without any remainder.
Methods to Notice GCF of 15 and 64
The methods to find the GCF of 15 and 64 are explained below.
 Using Euclid’s Algorithm
 Prime Factorization Method
 Listing Mutual Factors
GCF of 15 and 64 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(10, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Hither X = 64 and Y = 15
 GCF(64, fifteen) = GCF(fifteen, 64 mod 15) = GCF(15, 4)
 GCF(15, 4) = GCF(four, fifteen modern 4) = GCF(4, 3)
 GCF(iv, 3) = GCF(3, 4 mod three) = GCF(iii, i)
 GCF(3, 1) = i (∵ GCF(X, 1) = i)
Therefore, the value of GCF of xv and 64 is 1.
GCF of xv and 64 past Prime Factorization
Prime number factorization of 15 and 64 is (3 × 5) and (2 × 2 × 2 × two × ii × 2) respectively. Equally visible, there are no mutual prime factors between 15 and 64, i.e. they are coprime. Hence, the GCF of 15 and 64 will be 1.
GCF of fifteen and 64 by Listing Common Factors

Factors of 15:
one, iii, 5, xv 
Factors of 64:
1, 2, 4, viii, 16, 32, 64
Since, ane is the but common cistron between 15 and 64. The Greatest Common Factor of fifteen and 64 is ane.
☛ Also Check:
 GCF of twenty and 36 = four
 GCF of 60 and seventy = 10
 GCF of 48 and 16 = xvi
 GCF of 12 and 32 = four
 GCF of 32 and lx = 4
 GCF of 12 and eighteen = 6
 GCF of 32 and 36 = 4
GCF of 15 and 64 Examples

Example ane: Find the GCF of xv and 64, if their LCM is 960.
Solution:
∵ LCM × GCF = xv × 64
⇒ GCF(15, 64) = (15 × 64)/960 = 1
Therefore, the greatest common gene of xv and 64 is one. 
Example 2: Find the greatest number that divides 15 and 64 exactly.
Solution:
The greatest number that divides 15 and 64 exactly is their greatest common cistron, i.e. GCF of 15 and 64.
⇒ Factors of fifteen and 64: Factors of xv = i, three, five, fifteen
 Factors of 64 = 1, 2, four, 8, 16, 32, 64
Therefore, the GCF of 15 and 64 is 1.

Instance 3: For ii numbers, GCF = one and LCM = 960. If ane number is 15, find the other number.
Solution:
Given: GCF (x, 15) = 1 and LCM (x, 15) = 960
∵ GCF × LCM = fifteen × (x)
⇒ x = (GCF × LCM)/15
⇒ x = (1 × 960)/15
⇒ x = 64
Therefore, the other number is 64.
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FAQs on GCF of 15 and 64
What is the GCF of 15 and 64?
The
GCF of fifteen and 64 is 1
. To calculate the GCF (Greatest Common Factor) of fifteen and 64, we need to cistron each number (factors of 15 = one, 3, 5, 15; factors of 64 = i, ii, 4, 8, 16, 32, 64) and choose the greatest cistron that exactly divides both xv and 64, i.e., ane.
How to Find the GCF of fifteen and 64 by Prime number Factorization?
To find the GCF of xv and 64, nosotros volition notice the prime factorization of the given numbers, i.e. fifteen = three × five; 64 = 2 × ii × 2 × 2 × 2 × 2.
⇒ There is no common prime number gene for xv and 64. Hence, GCF (15, 64) = one.
☛ Prime Numbers
If the GCF of 64 and xv is 1, Discover its LCM.
GCF(64, 15) × LCM(64, 15) = 64 × fifteen
Since the GCF of 64 and 15 = 1
⇒ one × LCM(64, 15) = 960
Therefore, LCM = 960
☛ Greatest Common Factor Calculator
What is the Relation Betwixt LCM and GCF of xv, 64?
The following equation tin be used to express the relation between LCM and GCF of 15 and 64, i.e. GCF × LCM = 15 × 64.
How to Find the GCF of 15 and 64 past Long Partition Method?
To observe the GCF of xv, 64 using long segmentation method, 64 is divided past 15. The corresponding divisor (i) when residue equals 0 is taken as GCF.
What are the Methods to Find GCF of 15 and 64?
There are three commonly used methods to find the
GCF of fifteen and 64.
 By Long Division
 By Prime Factorization
 By List Mutual Factors
What is the Greatest Common Factor of 15 and 64
Source: https://www.cuemath.com/numbers/gcfof15and64/#:~:text=The%20Greatest%20Common%20Factor%20of%2015%20and%2064%20is%201.
Originally posted 20220807 18:22:52.