GCF of 58 and 87
GCF of 58 and 87 is the largest possible number that divides 58 and 87 exactly without any remainder. The factors of 58 and 87 are 1, 2, 29, 58 and 1, 3, 29, 87 respectively. There are 3 commonly used methods to find the GCF of 58 and 87 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 58 and 87 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 58 and 87?
Answer: GCF of 58 and 87 is 29.
Explanation:
The GCF of two non-zero integers, x(58) and y(87), is the greatest positive integer m(29) that divides both x(58) and y(87) without any remainder.
Methods to Find GCF of 58 and 87
Let's look at the different methods for finding the GCF of 58 and 87.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 58 and 87 by Prime Factorization
Prime factorization of 58 and 87 is (2 × 29) and (3 × 29) respectively. As visible, 58 and 87 have only one common prime factor i.e. 29. Hence, the GCF of 58 and 87 is 29.
GCF of 58 and 87 by Listing Common Factors
- Factors of 58: 1, 2, 29, 58
- Factors of 87: 1, 3, 29, 87
There are 2 common factors of 58 and 87, that are 1 and 29. Therefore, the greatest common factor of 58 and 87 is 29.
GCF of 58 and 87 by Long Division
GCF of 58 and 87 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 87 (larger number) by 58 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (58) by the remainder (29).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (29) is the GCF of 58 and 87.
☛ Also Check:
- GCF of 32 and 81 = 1
- GCF of 42 and 90 = 6
- GCF of 33 and 66 = 33
- GCF of 30 and 72 = 6
- GCF of 2 and 7 = 1
- GCF of 28 and 98 = 14
- GCF of 18 and 60 = 6
FAQs on GCF of 58 and 87
What is the GCF of 58 and 87?
The GCF of 58 and 87 is 29. To calculate the GCF (Greatest Common Factor) of 58 and 87, we need to factor each number (factors of 58 = 1, 2, 29, 58; factors of 87 = 1, 3, 29, 87) and choose the greatest factor that exactly divides both 58 and 87, i.e., 29.
How to Find the GCF of 58 and 87 by Prime Factorization?
To find the GCF of 58 and 87, we will find the prime factorization of the given numbers, i.e. 58 = 2 × 29; 87 = 3 × 29.
⇒ Since 29 is the only common prime factor of 58 and 87. Hence, GCF (58, 87) = 29.
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 58, 87?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 58 and 87, i.e. GCF × LCM = 58 × 87.
What are the Methods to Find GCF of 58 and 87?
There are three commonly used methods to find the GCF of 58 and 87.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
If the GCF of 87 and 58 is 29, Find its LCM.
GCF(87, 58) × LCM(87, 58) = 87 × 58
Since the GCF of 87 and 58 = 29
⇒ 29 × LCM(87, 58) = 5046
Therefore, LCM = 174
☛ GCF Calculator
How to Find the GCF of 58 and 87 by Long Division Method?
To find the GCF of 58, 87 using long division method, 87 is divided by 58. The corresponding divisor (29) when remainder equals 0 is taken as GCF.