Highest Common Factor of 336, 867, 337 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 336, 867, 337 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 867, 337 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 336, 867, 337 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 336, 867, 337 is 1.
HCF(336, 867, 337) = 1
HCF of 336, 867, 337 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 867, 337 is 1.
Highest Common Factor of 336,867,337 is 1
Step 1: Since 867 > 336, we apply the division lemma to 867 and 336, to get
867 = 336 x 2 + 195
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 195 and 336, to get
336 = 195 x 1 + 141
Step 3: We consider the new divisor 195 and the new remainder 141, and apply the division lemma to get
195 = 141 x 1 + 54
We consider the new divisor 141 and the new remainder 54,and apply the division lemma to get
141 = 54 x 2 + 33
We consider the new divisor 54 and the new remainder 33,and apply the division lemma to get
54 = 33 x 1 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 336 and 867 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(54,33) = HCF(141,54) = HCF(195,141) = HCF(336,195) = HCF(867,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 337 > 3, we apply the division lemma to 337 and 3, to get
337 = 3 x 112 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 337 is 1
Notice that 1 = HCF(3,1) = HCF(337,3) .
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Frequently Asked Questions on HCF of 336, 867, 337 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 336, 867, 337?
Answer: HCF of 336, 867, 337 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 867, 337 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 867, 337 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.