Highest Common Factor of 906, 137, 685 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 906, 137, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 137, 685 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 906, 137, 685 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 906, 137, 685 is 1.
HCF(906, 137, 685) = 1
HCF of 906, 137, 685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 906, 137, 685 is 1.
Highest Common Factor of 906,137,685 is 1
Step 1: Since 906 > 137, we apply the division lemma to 906 and 137, to get
906 = 137 x 6 + 84
Step 2: Since the reminder 137 ≠ 0, we apply division lemma to 84 and 137, to get
137 = 84 x 1 + 53
Step 3: We consider the new divisor 84 and the new remainder 53, and apply the division lemma to get
84 = 53 x 1 + 31
We consider the new divisor 53 and the new remainder 31,and apply the division lemma to get
53 = 31 x 1 + 22
We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get
31 = 22 x 1 + 9
We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get
22 = 9 x 2 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 906 and 137 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(53,31) = HCF(84,53) = HCF(137,84) = HCF(906,137) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 1, we apply the division lemma to 685 and 1, to get
685 = 1 x 685 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 685 is 1
Notice that 1 = HCF(685,1) .
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Frequently Asked Questions on HCF of 906, 137, 685 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 906, 137, 685?
Answer: HCF of 906, 137, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 137, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 137, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
