### 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.

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**HCF of 50 and 60 Using the Listing Factor Method**

**T**o 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.

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**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.

Written by

Prerit Jain