GCF of 24 and 35
GCF of 24 and 35 is the largest possible number that divides 24 and 35 exactly without any remainder. The factors of 24 and 35 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 24 and 35 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 24 and 35 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 24 and 35?
Answer: GCF of 24 and 35 is 1.
Explanation:
The GCF of two non-zero integers, x(24) and y(35), is the greatest positive integer m(1) that divides both x(24) and y(35) without any remainder.
Methods to Find GCF of 24 and 35
Let's look at the different methods for finding the GCF of 24 and 35.
- Using Euclid's Algorithm
- Prime Factorization Method
- Long Division Method
GCF of 24 and 35 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 = 35 and Y = 24
- GCF(35, 24) = GCF(24, 35 mod 24) = GCF(24, 11)
- GCF(24, 11) = GCF(11, 24 mod 11) = GCF(11, 2)
- GCF(11, 2) = GCF(2, 11 mod 2) = GCF(2, 1)
- GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)
Therefore, the value of GCF of 24 and 35 is 1.
GCF of 24 and 35 by Prime Factorization
Prime factorization of 24 and 35 is (2 × 2 × 2 × 3) and (5 × 7) respectively. As visible, there are no common prime factors between 24 and 35, i.e. they are co-prime. Hence, the GCF of 24 and 35 will be 1.
GCF of 24 and 35 by Long Division
GCF of 24 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 35 (larger number) by 24 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (11).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 24 and 35.
☛ Also Check:
- GCF of 14 and 42 = 14
- GCF of 28 and 98 = 14
- GCF of 12 and 15 = 3
- GCF of 45 and 120 = 15
- GCF of 24 and 96 = 24
- GCF of 32 and 81 = 1
- GCF of 20 and 30 = 10
FAQs on GCF of 24 and 35
What is the GCF of 24 and 35?
The GCF of 24 and 35 is 1. To calculate the greatest common factor of 24 and 35, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 24 and 35, i.e., 1.
How to Find the GCF of 24 and 35 by Prime Factorization?
To find the GCF of 24 and 35, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 35 = 5 × 7.
⇒ There is no common prime factor for 24 and 35. Hence, GCF (24, 35) = 1.
☛ Prime Numbers
What are the Methods to Find GCF of 24 and 35?
There are three commonly used methods to find the GCF of 24 and 35.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
What is the Relation Between LCM and GCF of 24, 35?
The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 35, i.e. GCF × LCM = 24 × 35.
How to Find the GCF of 24 and 35 by Long Division Method?
To find the GCF of 24, 35 using long division method, 35 is divided by 24. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
If the GCF of 35 and 24 is 1, Find its LCM.
GCF(35, 24) × LCM(35, 24) = 35 × 24
Since the GCF of 35 and 24 = 1
⇒ 1 × LCM(35, 24) = 840
Therefore, LCM = 840
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