Highest Common Factor of 694, 498, 400 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 694, 498, 400 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 498, 400 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 694, 498, 400 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, 498, 400 is 2.
HCF(694, 498, 400) = 2
HCF of 694, 498, 400 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 498, 400 is 2.
Highest Common Factor of 694,498,400 is 2
Step 1: Since 694 > 498, we apply the division lemma to 694 and 498, to get
694 = 498 x 1 + 196
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 196 and 498, to get
498 = 196 x 2 + 106
Step 3: We consider the new divisor 196 and the new remainder 106, and apply the division lemma to get
196 = 106 x 1 + 90
We consider the new divisor 106 and the new remainder 90,and apply the division lemma to get
106 = 90 x 1 + 16
We consider the new divisor 90 and the new remainder 16,and apply the division lemma to get
90 = 16 x 5 + 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 498 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(90,16) = HCF(106,90) = HCF(196,106) = HCF(498,196) = HCF(694,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 400 > 2, we apply the division lemma to 400 and 2, to get
400 = 2 x 200 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 400 is 2
Notice that 2 = HCF(400,2) .
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Frequently Asked Questions on HCF of 694, 498, 400 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 694, 498, 400?
Answer: HCF of 694, 498, 400 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 498, 400 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 498, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.