Highest Common Factor of 837, 3069, 9042 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, 3069, 9042 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 3069, 9042 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, 3069, 9042 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, 3069, 9042 is 3.
HCF(837, 3069, 9042) = 3
HCF of 837, 3069, 9042 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, 3069, 9042 is 3.
Highest Common Factor of 837,3069,9042 is 3
Step 1: Since 3069 > 837, we apply the division lemma to 3069 and 837, to get
3069 = 837 x 3 + 558
Step 2: Since the reminder 837 ≠ 0, we apply division lemma to 558 and 837, to get
837 = 558 x 1 + 279
Step 3: We consider the new divisor 558 and the new remainder 279, and apply the division lemma to get
558 = 279 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 279, the HCF of 837 and 3069 is 279
Notice that 279 = HCF(558,279) = HCF(837,558) = HCF(3069,837) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9042 > 279, we apply the division lemma to 9042 and 279, to get
9042 = 279 x 32 + 114
Step 2: Since the reminder 279 ≠ 0, we apply division lemma to 114 and 279, to get
279 = 114 x 2 + 51
Step 3: We consider the new divisor 114 and the new remainder 51, and apply the division lemma to get
114 = 51 x 2 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 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 279 and 9042 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(114,51) = HCF(279,114) = HCF(9042,279) .
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Frequently Asked Questions on HCF of 837, 3069, 9042 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, 3069, 9042?
Answer: HCF of 837, 3069, 9042 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 3069, 9042 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 3069, 9042 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.