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 377, 613, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 377, 613, 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 377, 613, 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 377, 613, 209 is 1.
HCF(377, 613, 209) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 377, 613, 209 is 1.
Step 1: Since 613 > 377, we apply the division lemma to 613 and 377, to get
613 = 377 x 1 + 236
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 236 and 377, to get
377 = 236 x 1 + 141
Step 3: We consider the new divisor 236 and the new remainder 141, and apply the division lemma to get
236 = 141 x 1 + 95
We consider the new divisor 141 and the new remainder 95,and apply the division lemma to get
141 = 95 x 1 + 46
We consider the new divisor 95 and the new remainder 46,and apply the division lemma to get
95 = 46 x 2 + 3
We consider the new divisor 46 and the new remainder 3,and apply the division lemma to get
46 = 3 x 15 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 377 and 613 is 1
Notice that 1 = HCF(3,1) = HCF(46,3) = HCF(95,46) = HCF(141,95) = HCF(236,141) = HCF(377,236) = HCF(613,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get
209 = 1 x 209 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1
Notice that 1 = HCF(209,1) .
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 377, 613, 209?
Answer: HCF of 377, 613, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 377, 613, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 377, 613, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.