HCF of 56 and 84

The HCF of 56 and 84 is 28. As the name goes as highest common factor, HCF of the number is obtained by taking the largest factor or divisor for the given numbers. The methods that are widely used to find the HCF of the number are:

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

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HCF of 56 and 84 Using the Long Division Method

If you want to find the HCF of a number fastly with accuracy then the long division method is the correct box to be checked.
Step 1: Divide the greater digit by a smaller digit
Step 2: The last divisor from which zero is obtained is the HCF of the number.
Therefore, the HCF of 56 and 84 using the long division method.
Step 1: Divide the greater digit by a smaller digit.

Step 2: The last divisor from which zero is obtained is the HCF of the number.
The corresponding divisor is 28.
Hence the HCF(56,84) = 28.

HCF of 56 and 84 Using the Prime Factorization Method

The factors that are prime numbers and not composite are used to find the HCF of the given numbers.

Step 1: Find the prime factors of the given numbers
Step 2: List the common prime factors
Step 3: Multiply the common prime factors which are the HCF of the given numbers. 
Therefore, the HCF of 56 and 84 using the prime factorization method
Step 1: Find the prime factors of the given numbers
The prime factors of 56 = 2 × 2 × 2 × 7 
The prime factors of 84 = 2 × 2 × 3× 7 
Step 2: List the common prime factors
The common prime factors =  2 × 2 × 7
Step 3: Multiply the common prime factors which are the HCF of the given numbers. 
 By multiplying the common prime numbers we get 28
Hence, HCF(56,84) = 28

HCF of 56 and 84 Using the Listing Factor Method

The listing factor method pics out the largest digit that is the factor of 56 and 84, thus determining the HCF of the number.

Step 1: Find the factors and list the common factors
Step 2: The largest factor that is common is the HCF of the given number.
Therefore, the HCF of 56 and 84 using the listing factor method is as given below:
Step 1: Find the factors and list the common factors
The factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56 
The factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The common factors are 1,2,4,7,14 and 28
Step 2: The largest factor that is common is the HCF of the given number.
The factor that is the largest among the six factors is 28.
Hence, HCF(56,84) = 28

Solved Examples:

Example 1: What are the HCF and LCM of 56 and 84?
The HCF of (56,84) = 28
The LCM of (56,84) = 168

Example 2: What is the HCF of 56 and 84 using the prime factorization method?
The prime factors of 56 = 2 × 2 × 2 × 7 
The prime factors of 84 = 2 × 2 × 3× 7 
The HCF of  (56,84) = 28

Example 3: If the product of two numbers is 4704 and their HCF is 28. Find their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 4704  ∕ 28
Hence LCM = 168.

Example 4:There are two numbers whose LCM and HCF are given find another number
LCM of the number = 168
HCF of the number = 28.
The number is given = 56
HCF (56,x) = 28
LCM(56,x) = 168
Therefore, LCM×HCF = (X)×56
 X = (LCM × HCF) ∕ 56
Hence, 
X = (168× 28)  ∕ 56
Therefore, X = 84 is the other number.

Example 5: What is the HCF of 56 and 84 if their LCM is 168?
The HCF (56,84 ) = 28.

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Frequently Asked Questions (FAQ)

What are the LCM and HCF of 56 and 84, and find the product of 56 and 84?
The LCM of 56 and 84 = 168
The HCF of 56 and 84 = 28
The product of 56 and 84 = 4704

Find the HCF of 56 and 84 by the listing factor method.
The factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56 
The factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The HCF of  (56,84) = 28

Find the HCF of 12 and 18.
The HCF (12,18) = 6

Find the HCF of 56 and 84 by the division method.

HCF (56,84) = 28.