Highest Common Factor of 993, 9675, 1096 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 993, 9675, 1096 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 993, 9675, 1096 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 993, 9675, 1096 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 993, 9675, 1096 is 1.
HCF(993, 9675, 1096) = 1
HCF of 993, 9675, 1096 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 993, 9675, 1096 is 1.
Highest Common Factor of 993,9675,1096 is 1
Step 1: Since 9675 > 993, we apply the division lemma to 9675 and 993, to get
9675 = 993 x 9 + 738
Step 2: Since the reminder 993 ≠ 0, we apply division lemma to 738 and 993, to get
993 = 738 x 1 + 255
Step 3: We consider the new divisor 738 and the new remainder 255, and apply the division lemma to get
738 = 255 x 2 + 228
We consider the new divisor 255 and the new remainder 228,and apply the division lemma to get
255 = 228 x 1 + 27
We consider the new divisor 228 and the new remainder 27,and apply the division lemma to get
228 = 27 x 8 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 993 and 9675 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(228,27) = HCF(255,228) = HCF(738,255) = HCF(993,738) = HCF(9675,993) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1096 > 3, we apply the division lemma to 1096 and 3, to get
1096 = 3 x 365 + 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 1096 is 1
Notice that 1 = HCF(3,1) = HCF(1096,3) .
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Frequently Asked Questions on HCF of 993, 9675, 1096 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 993, 9675, 1096?
Answer: HCF of 993, 9675, 1096 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 993, 9675, 1096 using Euclid's Algorithm?
Answer: For arbitrary numbers 993, 9675, 1096 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.