Highest Common Factor of 978, 812, 698 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 978, 812, 698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 812, 698 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 978, 812, 698 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 978, 812, 698 is 2.
HCF(978, 812, 698) = 2
HCF of 978, 812, 698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 812, 698 is 2.
Highest Common Factor of 978,812,698 is 2
Step 1: Since 978 > 812, we apply the division lemma to 978 and 812, to get
978 = 812 x 1 + 166
Step 2: Since the reminder 812 ≠ 0, we apply division lemma to 166 and 812, to get
812 = 166 x 4 + 148
Step 3: We consider the new divisor 166 and the new remainder 148, and apply the division lemma to get
166 = 148 x 1 + 18
We consider the new divisor 148 and the new remainder 18,and apply the division lemma to get
148 = 18 x 8 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 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 978 and 812 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(148,18) = HCF(166,148) = HCF(812,166) = HCF(978,812) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 2, we apply the division lemma to 698 and 2, to get
698 = 2 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 698 is 2
Notice that 2 = HCF(698,2) .
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Frequently Asked Questions on HCF of 978, 812, 698 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 978, 812, 698?
Answer: HCF of 978, 812, 698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 812, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 812, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.