Highest Common Factor of 762, 441, 69 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 762, 441, 69 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 441, 69 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 762, 441, 69 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 762, 441, 69 is 3.
HCF(762, 441, 69) = 3
HCF of 762, 441, 69 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 762, 441, 69 is 3.
Highest Common Factor of 762,441,69 is 3
Step 1: Since 762 > 441, we apply the division lemma to 762 and 441, to get
762 = 441 x 1 + 321
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 321 and 441, to get
441 = 321 x 1 + 120
Step 3: We consider the new divisor 321 and the new remainder 120, and apply the division lemma to get
321 = 120 x 2 + 81
We consider the new divisor 120 and the new remainder 81,and apply the division lemma to get
120 = 81 x 1 + 39
We consider the new divisor 81 and the new remainder 39,and apply the division lemma to get
81 = 39 x 2 + 3
We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 762 and 441 is 3
Notice that 3 = HCF(39,3) = HCF(81,39) = HCF(120,81) = HCF(321,120) = HCF(441,321) = HCF(762,441) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 3, we apply the division lemma to 69 and 3, to get
69 = 3 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 69 is 3
Notice that 3 = HCF(69,3) .
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Frequently Asked Questions on HCF of 762, 441, 69 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 762, 441, 69?
Answer: HCF of 762, 441, 69 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 441, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 441, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.