GCF of 25 and 36
GCF of 25 and 36 is the largest possible number that divides 25 and 36 exactly without any remainder. The factors of 25 and 36 are 1, 5, 25 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 25 and 36 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 25 and 36 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 25 and 36?
Answer: GCF of 25 and 36 is 1.
Explanation:
The GCF of two non-zero integers, x(25) and y(36), is the greatest positive integer m(1) that divides both x(25) and y(36) without any remainder.
Methods to Find GCF of 25 and 36
Let's look at the different methods for finding the GCF of 25 and 36.
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 25 and 36 by Prime Factorization
Prime factorization of 25 and 36 is (5 × 5) and (2 × 2 × 3 × 3) respectively. As visible, there are no common prime factors between 25 and 36, i.e. they are coprime. Hence, the GCF of 25 and 36 will be 1.
GCF of 25 and 36 by Long Division
GCF of 25 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 36 (larger number) by 25 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (11).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 25 and 36.
GCF of 25 and 36 by Listing Common Factors
- Factors of 25: 1, 5, 25
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Since, 1 is the only common factor between 25 and 36. The Greatest Common Factor of 25 and 36 is 1.
☛ Also Check:
- GCF of 25 and 45 = 5
- GCF of 20 and 32 = 4
- GCF of 3 and 9 = 3
- GCF of 35 and 50 = 5
- GCF of 8 and 24 = 8
- GCF of 49 and 63 = 7
- GCF of 30 and 72 = 6
FAQs on GCF of 25 and 36
What is the GCF of 25 and 36?
The GCF of 25 and 36 is 1. To calculate the GCF (Greatest Common Factor) of 25 and 36, we need to factor each number (factors of 25 = 1, 5, 25; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 25 and 36, i.e., 1.
How to Find the GCF of 25 and 36 by Prime Factorization?
To find the GCF of 25 and 36, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 36 = 2 × 2 × 3 × 3.
⇒ There is no common prime factor for 25 and 36. Hence, GCF (25, 36) = 1.
☛ What is a Prime Number?
What are the Methods to Find GCF of 25 and 36?
There are three commonly used methods to find the GCF of 25 and 36.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
If the GCF of 36 and 25 is 1, Find its LCM.
GCF(36, 25) × LCM(36, 25) = 36 × 25
Since the GCF of 36 and 25 = 1
⇒ 1 × LCM(36, 25) = 900
Therefore, LCM = 900
☛ Greatest Common Factor Calculator
How to Find the GCF of 25 and 36 by Long Division Method?
To find the GCF of 25, 36 using long division method, 36 is divided by 25. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 25, 36?
The following equation can be used to express the relation between LCM and GCF of 25 and 36, i.e. GCF × LCM = 25 × 36.