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 694, 814, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 814, 559 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 694, 814, 559 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 694, 814, 559 is 1.
HCF(694, 814, 559) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 814, 559 is 1.
Step 1: Since 814 > 694, we apply the division lemma to 814 and 694, to get
814 = 694 x 1 + 120
Step 2: Since the reminder 694 ≠ 0, we apply division lemma to 120 and 694, to get
694 = 120 x 5 + 94
Step 3: We consider the new divisor 120 and the new remainder 94, and apply the division lemma to get
120 = 94 x 1 + 26
We consider the new divisor 94 and the new remainder 26,and apply the division lemma to get
94 = 26 x 3 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 694 and 814 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(94,26) = HCF(120,94) = HCF(694,120) = HCF(814,694) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 559 > 2, we apply the division lemma to 559 and 2, to get
559 = 2 x 279 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 559 is 1
Notice that 1 = HCF(2,1) = HCF(559,2) .
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 694, 814, 559?
Answer: HCF of 694, 814, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 814, 559 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 814, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.