Highest Common Factor of 706, 906, 216, 32 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 706, 906, 216, 32 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 906, 216, 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 706, 906, 216, 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 706, 906, 216, 32 is 2.
HCF(706, 906, 216, 32) = 2
HCF of 706, 906, 216, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 706, 906, 216, 32 is 2.
Highest Common Factor of 706,906,216,32 is 2
Step 1: Since 906 > 706, we apply the division lemma to 906 and 706, to get
906 = 706 x 1 + 200
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 200 and 706, to get
706 = 200 x 3 + 106
Step 3: We consider the new divisor 200 and the new remainder 106, and apply the division lemma to get
200 = 106 x 1 + 94
We consider the new divisor 106 and the new remainder 94,and apply the division lemma to get
106 = 94 x 1 + 12
We consider the new divisor 94 and the new remainder 12,and apply the division lemma to get
94 = 12 x 7 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 906 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(94,12) = HCF(106,94) = HCF(200,106) = HCF(706,200) = HCF(906,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 2, we apply the division lemma to 216 and 2, to get
216 = 2 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 216 is 2
Notice that 2 = HCF(216,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 2, we apply the division lemma to 32 and 2, to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 32 is 2
Notice that 2 = HCF(32,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 706, 906, 216, 32 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 706, 906, 216, 32?
Answer: HCF of 706, 906, 216, 32 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 906, 216, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 906, 216, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.