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 921, 606, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 606, 209 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 921, 606, 209 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 921, 606, 209 is 1.
HCF(921, 606, 209) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 606, 209 is 1.
Step 1: Since 921 > 606, we apply the division lemma to 921 and 606, to get
921 = 606 x 1 + 315
Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 315 and 606, to get
606 = 315 x 1 + 291
Step 3: We consider the new divisor 315 and the new remainder 291, and apply the division lemma to get
315 = 291 x 1 + 24
We consider the new divisor 291 and the new remainder 24,and apply the division lemma to get
291 = 24 x 12 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 921 and 606 is 3
Notice that 3 = HCF(24,3) = HCF(291,24) = HCF(315,291) = HCF(606,315) = HCF(921,606) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 3, we apply the division lemma to 209 and 3, to get
209 = 3 x 69 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 209 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(209,3) .
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 921, 606, 209?
Answer: HCF of 921, 606, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 606, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 606, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.