HCF of 50 and 60

The greatest common factor (GCF) of 50 and 60 is 10. That is the number 10 divides both 50 and 60 equally and entirely leaving the remainder zero. There are 3 main common methods to find the GCF or HCF of the given number.

• Listing Factor Method
• Long Division Method
• Prime Factorization Method.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

HCF of 50 and 60 Using the Listing Factor Method

To find the HCF using the listing factor method the common factors are picked out from both the numbers and the largest of them is the HCF o the number.

Step 1: Find the factors 
Step 2: List the common factors
Step 3: The largest of them is the HCF of the given number
Therefore, the HCF of 50 and 60 using the listing factor method
Step 1: Find the factors 
The factors of 50 = 1, 2, 5, 10, 25, 50
The factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Step 2: List the common factors
The common factors are 1,2,5 and 10.
Step 3: The largest of them is the HCF of the given number
The largest of them all is 10
Hence, HCF(50,60) = 10

HCF of 50 and 60 Using the Long Division Method

Dividing the larger number that is 60 by the smallest number 50 gives the HCF of the number. The last corresponding divisor is the HCF of the number.

Step 1: Divide the larger number by a smaller number
Step 2: The corresponding divisor is the HCF of the number
Therefore, HCF of 50 and 60 using the long division method is as follows:
Step 1: Divide the larger number by a smaller number

Step 2: The corresponding divisor is the HCF of the number
The corresponding divisor is 10
Hence, HCF(50.60) = 10

HCF of 50 and 60 Using the Prime Factorization Method

Prime factorization mainly considers the factors that are prime and not composite. To find the HCF of 50 and 60 using the prime factorization method the following steps are carried out.

Step 1: Find the prime factors and pick the common prime factors
Step 2: Multiply the common prime factors which are the HCF of the given number
Therefore, the HCF of 50 and 60 using the prime factorization method is as follows:
Step 1: Find the prime factors and pick the common prime factors
The prime factor of 50 = 2 × 5 × 5
The prime factor of 60 = 2 × 2 × 3 × 5
The common prime factors = 2 × 5
Step 2: Multiply the common prime factors which are the HCF of the given number
Multiplying the two numbers we get 10
Hence, the HCF(50,60) = 10

Solved Examples:

Example 1: What are the HCF and LCM of 50 and 60?
The HCF of (50,60) = 10
The LCM of (50.60) = 300

Example 2: What is the HCF of 50 and 60 using the prime factorization method?
The prime factor of 50 = 2 × 5 × 5
The prime factor of 60 = 2 × 2 × 3 × 5
The HCF of  (50,60) = 10

Example 3: If the product of two numbers is 3000 and their HCF is 10. Find their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 3000 ∕ 10
Hence LCM = 300.

Example 4:There are two numbers whose LCM and HCF are given find another number
LCM of the number = 300
HCF of the number = 10.
The number is given = 50
HCF (50,x) = 10
LCM(50,x) = 300
Therefore, LCM×HCF = (X)×50
 X = (LCM × HCF) ∕ 50
Hence, 
X = (10× 300)  ∕ 50
Therefore, X = 60 is the other number.

Example 5: What is the HCF of 50 and 60 if their LCM is 300?
The HCF (50,60 ) = 10.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

Frequently Asked Questions (FAQ)

What are the LCM and HCF of 50 and 60, and find the product of 50 and 60?
The LCM of 50 and 60 = 300
The HCF of 50 and 60 = 10
The product of 50 and 60 = 3000

Find the HCF of 50 and 60 by the listing factor method.
The factors of 50 = 1, 2, 5, 10, 25, 50
The factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The HCF of  (50,60) = 10

Find the HCF of 42 and 17.
The HCF (42,17) = 14

Find the HCF of 50 and 60 by the division method.

HCF (50,60) = 10.