Highest Common Factor of 912, 384, 340, 91 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 912, 384, 340, 91 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 384, 340, 91 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 912, 384, 340, 91 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 912, 384, 340, 91 is 1.
HCF(912, 384, 340, 91) = 1
HCF of 912, 384, 340, 91 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 384, 340, 91 is 1.
Highest Common Factor of 912,384,340,91 is 1
Step 1: Since 912 > 384, we apply the division lemma to 912 and 384, to get
912 = 384 x 2 + 144
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 144 and 384, to get
384 = 144 x 2 + 96
Step 3: We consider the new divisor 144 and the new remainder 96, and apply the division lemma to get
144 = 96 x 1 + 48
We consider the new divisor 96 and the new remainder 48, and apply the division lemma to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 912 and 384 is 48
Notice that 48 = HCF(96,48) = HCF(144,96) = HCF(384,144) = HCF(912,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 48, we apply the division lemma to 340 and 48, to get
340 = 48 x 7 + 4
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 4 and 48, to get
48 = 4 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 48 and 340 is 4
Notice that 4 = HCF(48,4) = HCF(340,48) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 91 > 4, we apply the division lemma to 91 and 4, to get
91 = 4 x 22 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 91 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(91,4) .
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Frequently Asked Questions on HCF of 912, 384, 340, 91 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 912, 384, 340, 91?
Answer: HCF of 912, 384, 340, 91 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 384, 340, 91 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 384, 340, 91 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.