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, 400, 869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 400, 869 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, 400, 869 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, 400, 869 is 1.
HCF(694, 400, 869) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 400, 869 is 1.
Step 1: Since 694 > 400, we apply the division lemma to 694 and 400, to get
694 = 400 x 1 + 294
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 294 and 400, to get
400 = 294 x 1 + 106
Step 3: We consider the new divisor 294 and the new remainder 106, and apply the division lemma to get
294 = 106 x 2 + 82
We consider the new divisor 106 and the new remainder 82,and apply the division lemma to get
106 = 82 x 1 + 24
We consider the new divisor 82 and the new remainder 24,and apply the division lemma to get
82 = 24 x 3 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 400 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(82,24) = HCF(106,82) = HCF(294,106) = HCF(400,294) = HCF(694,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 869 > 2, we apply the division lemma to 869 and 2, to get
869 = 2 x 434 + 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 869 is 1
Notice that 1 = HCF(2,1) = HCF(869,2) .
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, 400, 869?
Answer: HCF of 694, 400, 869 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 400, 869 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 400, 869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.