Highest Common Factor of 996, 698, 912, 82 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 996, 698, 912, 82 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 698, 912, 82 is 2 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 996, 698, 912, 82 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 996, 698, 912, 82 is 2.
HCF(996, 698, 912, 82) = 2
HCF of 996, 698, 912, 82 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 698, 912, 82 is 2.
Highest Common Factor of 996,698,912,82 is 2
Step 1: Since 996 > 698, we apply the division lemma to 996 and 698, to get
996 = 698 x 1 + 298
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 298 and 698, to get
698 = 298 x 2 + 102
Step 3: We consider the new divisor 298 and the new remainder 102, and apply the division lemma to get
298 = 102 x 2 + 94
We consider the new divisor 102 and the new remainder 94,and apply the division lemma to get
102 = 94 x 1 + 8
We consider the new divisor 94 and the new remainder 8,and apply the division lemma to get
94 = 8 x 11 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 996 and 698 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(94,8) = HCF(102,94) = HCF(298,102) = HCF(698,298) = HCF(996,698) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 2, we apply the division lemma to 912 and 2, to get
912 = 2 x 456 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 912 is 2
Notice that 2 = HCF(912,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 2, we apply the division lemma to 82 and 2, to get
82 = 2 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 82 is 2
Notice that 2 = HCF(82,2) .
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Frequently Asked Questions on HCF of 996, 698, 912, 82 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 996, 698, 912, 82?
Answer: HCF of 996, 698, 912, 82 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 698, 912, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 698, 912, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.