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 834, 804, 384, 32 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 834, 804, 384, 32 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 834, 804, 384, 32 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 834, 804, 384, 32 is 2.
HCF(834, 804, 384, 32) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 834, 804, 384, 32 is 2.
Step 1: Since 834 > 804, we apply the division lemma to 834 and 804, to get
834 = 804 x 1 + 30
Step 2: Since the reminder 804 ≠ 0, we apply division lemma to 30 and 804, to get
804 = 30 x 26 + 24
Step 3: We consider the new divisor 30 and the new remainder 24, and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 834 and 804 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(804,30) = HCF(834,804) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 384 > 6, we apply the division lemma to 384 and 6, to get
384 = 6 x 64 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 384 is 6
Notice that 6 = HCF(384,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 6, we apply the division lemma to 32 and 6, to get
32 = 6 x 5 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 32 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) .
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 834, 804, 384, 32?
Answer: HCF of 834, 804, 384, 32 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 834, 804, 384, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 834, 804, 384, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.