Highest Common Factor of 322, 766, 754 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 322, 766, 754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 766, 754 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 322, 766, 754 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 322, 766, 754 is 2.
HCF(322, 766, 754) = 2
HCF of 322, 766, 754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 766, 754 is 2.
Highest Common Factor of 322,766,754 is 2
Step 1: Since 766 > 322, we apply the division lemma to 766 and 322, to get
766 = 322 x 2 + 122
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 122 and 322, to get
322 = 122 x 2 + 78
Step 3: We consider the new divisor 122 and the new remainder 78, and apply the division lemma to get
122 = 78 x 1 + 44
We consider the new divisor 78 and the new remainder 44,and apply the division lemma to get
78 = 44 x 1 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 322 and 766 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(78,44) = HCF(122,78) = HCF(322,122) = HCF(766,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 754 > 2, we apply the division lemma to 754 and 2, to get
754 = 2 x 377 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 754 is 2
Notice that 2 = HCF(754,2) .
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Frequently Asked Questions on HCF of 322, 766, 754 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 322, 766, 754?
Answer: HCF of 322, 766, 754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 766, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 766, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.