Highest Common Factor of 837, 996, 15 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 837, 996, 15 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 996, 15 is 3 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 837, 996, 15 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 837, 996, 15 is 3.
HCF(837, 996, 15) = 3
HCF of 837, 996, 15 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 996, 15 is 3.
Highest Common Factor of 837,996,15 is 3
Step 1: Since 996 > 837, we apply the division lemma to 996 and 837, to get
996 = 837 x 1 + 159
Step 2: Since the reminder 837 ≠ 0, we apply division lemma to 159 and 837, to get
837 = 159 x 5 + 42
Step 3: We consider the new divisor 159 and the new remainder 42, and apply the division lemma to get
159 = 42 x 3 + 33
We consider the new divisor 42 and the new remainder 33,and apply the division lemma to get
42 = 33 x 1 + 9
We consider the new divisor 33 and the new remainder 9,and apply the division lemma to get
33 = 9 x 3 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 837 and 996 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(33,9) = HCF(42,33) = HCF(159,42) = HCF(837,159) = HCF(996,837) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 3, we apply the division lemma to 15 and 3, to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 15 is 3
Notice that 3 = HCF(15,3) .
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Frequently Asked Questions on HCF of 837, 996, 15 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 837, 996, 15?
Answer: HCF of 837, 996, 15 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 996, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 996, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.