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 182, 667, 712, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 182, 667, 712, 51 is 1 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 182, 667, 712, 51 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 182, 667, 712, 51 is 1.
HCF(182, 667, 712, 51) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 182, 667, 712, 51 is 1.
Step 1: Since 667 > 182, we apply the division lemma to 667 and 182, to get
667 = 182 x 3 + 121
Step 2: Since the reminder 182 ≠ 0, we apply division lemma to 121 and 182, to get
182 = 121 x 1 + 61
Step 3: We consider the new divisor 121 and the new remainder 61, and apply the division lemma to get
121 = 61 x 1 + 60
We consider the new divisor 61 and the new remainder 60,and apply the division lemma to get
61 = 60 x 1 + 1
We consider the new divisor 60 and the new remainder 1,and apply the division lemma to get
60 = 1 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 182 and 667 is 1
Notice that 1 = HCF(60,1) = HCF(61,60) = HCF(121,61) = HCF(182,121) = HCF(667,182) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 712 > 1, we apply the division lemma to 712 and 1, to get
712 = 1 x 712 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 712 is 1
Notice that 1 = HCF(712,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1
Notice that 1 = HCF(51,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 182, 667, 712, 51?
Answer: HCF of 182, 667, 712, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 182, 667, 712, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 182, 667, 712, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.