GCF of 46 and 69
GCF of 46 and 69 is the largest possible number that divides 46 and 69 exactly without any remainder. The factors of 46 and 69 are 1, 2, 23, 46 and 1, 3, 23, 69 respectively. There are 3 commonly used methods to find the GCF of 46 and 69 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 46 and 69 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 46 and 69?
Answer: GCF of 46 and 69 is 23.
Explanation:
The GCF of two non-zero integers, x(46) and y(69), is the greatest positive integer m(23) that divides both x(46) and y(69) without any remainder.
Methods to Find GCF of 46 and 69
Let's look at the different methods for finding the GCF of 46 and 69.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
GCF of 46 and 69 by Long Division
GCF of 46 and 69 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 69 (larger number) by 46 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (46) by the remainder (23).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (23) is the GCF of 46 and 69.
GCF of 46 and 69 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 69 and Y = 46
- GCF(69, 46) = GCF(46, 69 mod 46) = GCF(46, 23)
- GCF(46, 23) = GCF(23, 46 mod 23) = GCF(23, 0)
- GCF(23, 0) = 23 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 46 and 69 is 23.
GCF of 46 and 69 by Prime Factorization
Prime factorization of 46 and 69 is (2 × 23) and (3 × 23) respectively. As visible, 46 and 69 have only one common prime factor i.e. 23. Hence, the GCF of 46 and 69 is 23.
☛ Also Check:
- GCF of 25 and 90 = 5
- GCF of 36 and 96 = 12
- GCF of 24 and 80 = 8
- GCF of 64 and 144 = 16
- GCF of 28 and 32 = 4
- GCF of 10 and 35 = 5
- GCF of 16 and 56 = 8
FAQs on GCF of 46 and 69
What is the GCF of 46 and 69?
The GCF of 46 and 69 is 23. To calculate the GCF of 46 and 69, we need to factor each number (factors of 46 = 1, 2, 23, 46; factors of 69 = 1, 3, 23, 69) and choose the greatest factor that exactly divides both 46 and 69, i.e., 23.
What is the Relation Between LCM and GCF of 46, 69?
The following equation can be used to express the relation between LCM and GCF of 46 and 69, i.e. GCF × LCM = 46 × 69.
How to Find the GCF of 46 and 69 by Prime Factorization?
To find the GCF of 46 and 69, we will find the prime factorization of the given numbers, i.e. 46 = 2 × 23; 69 = 3 × 23.
⇒ Since 23 is the only common prime factor of 46 and 69. Hence, GCF (46, 69) = 23.
☛ What are Prime Numbers?
How to Find the GCF of 46 and 69 by Long Division Method?
To find the GCF of 46, 69 using long division method, 69 is divided by 46. The corresponding divisor (23) when remainder equals 0 is taken as GCF.
If the GCF of 69 and 46 is 23, Find its LCM.
GCF(69, 46) × LCM(69, 46) = 69 × 46
Since the GCF of 69 and 46 = 23
⇒ 23 × LCM(69, 46) = 3174
Therefore, LCM = 138
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 46 and 69?
There are three commonly used methods to find the GCF of 46 and 69.
- By Prime Factorization
- By Listing Common Factors
- By Long Division