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 762, 549, 184 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 549, 184 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 762, 549, 184 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 762, 549, 184 is 1.
HCF(762, 549, 184) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 762, 549, 184 is 1.
Step 1: Since 762 > 549, we apply the division lemma to 762 and 549, to get
762 = 549 x 1 + 213
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 213 and 549, to get
549 = 213 x 2 + 123
Step 3: We consider the new divisor 213 and the new remainder 123, and apply the division lemma to get
213 = 123 x 1 + 90
We consider the new divisor 123 and the new remainder 90,and apply the division lemma to get
123 = 90 x 1 + 33
We consider the new divisor 90 and the new remainder 33,and apply the division lemma to get
90 = 33 x 2 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 762 and 549 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(123,90) = HCF(213,123) = HCF(549,213) = HCF(762,549) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 184 > 3, we apply the division lemma to 184 and 3, to get
184 = 3 x 61 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 184 is 1
Notice that 1 = HCF(3,1) = HCF(184,3) .
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 762, 549, 184?
Answer: HCF of 762, 549, 184 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 549, 184 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 549, 184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.