Highest Common Factor of 697, 441, 978 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 697, 441, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 697, 441, 978 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 697, 441, 978 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 697, 441, 978 is 1.
HCF(697, 441, 978) = 1
HCF of 697, 441, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 697, 441, 978 is 1.
Highest Common Factor of 697,441,978 is 1
Step 1: Since 697 > 441, we apply the division lemma to 697 and 441, to get
697 = 441 x 1 + 256
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 256 and 441, to get
441 = 256 x 1 + 185
Step 3: We consider the new divisor 256 and the new remainder 185, and apply the division lemma to get
256 = 185 x 1 + 71
We consider the new divisor 185 and the new remainder 71,and apply the division lemma to get
185 = 71 x 2 + 43
We consider the new divisor 71 and the new remainder 43,and apply the division lemma to get
71 = 43 x 1 + 28
We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get
43 = 28 x 1 + 15
We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get
28 = 15 x 1 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 697 and 441 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(71,43) = HCF(185,71) = HCF(256,185) = HCF(441,256) = HCF(697,441) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 1, we apply the division lemma to 978 and 1, to get
978 = 1 x 978 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 978 is 1
Notice that 1 = HCF(978,1) .
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Frequently Asked Questions on HCF of 697, 441, 978 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 697, 441, 978?
Answer: HCF of 697, 441, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 697, 441, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 697, 441, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.