Highest Common Factor of 56, 84, 74, 746 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 56, 84, 74, 746 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 56, 84, 74, 746 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 56, 84, 74, 746 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 56, 84, 74, 746 is 2.
HCF(56, 84, 74, 746) = 2
HCF of 56, 84, 74, 746 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 56, 84, 74, 746 is 2.
Highest Common Factor of 56,84,74,746 is 2
Step 1: Since 84 > 56, we apply the division lemma to 84 and 56, to get
84 = 56 x 1 + 28
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 28 and 56, to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 56 and 84 is 28
Notice that 28 = HCF(56,28) = HCF(84,56) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 28, we apply the division lemma to 74 and 28, to get
74 = 28 x 2 + 18
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 18 and 28, to get
28 = 18 x 1 + 10
Step 3: We consider the new divisor 18 and the new remainder 10, and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 28 and 74 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(74,28) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 746 > 2, we apply the division lemma to 746 and 2, to get
746 = 2 x 373 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 746 is 2
Notice that 2 = HCF(746,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 56, 84, 74, 746 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 56, 84, 74, 746?
Answer: HCF of 56, 84, 74, 746 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 56, 84, 74, 746 using Euclid's Algorithm?
Answer: For arbitrary numbers 56, 84, 74, 746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.