Highest Common Factor of 774, 215, 742 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 774, 215, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 215, 742 is 1 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 774, 215, 742 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 774, 215, 742 is 1.
HCF(774, 215, 742) = 1
HCF of 774, 215, 742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 215, 742 is 1.
Highest Common Factor of 774,215,742 is 1
Step 1: Since 774 > 215, we apply the division lemma to 774 and 215, to get
774 = 215 x 3 + 129
Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 129 and 215, to get
215 = 129 x 1 + 86
Step 3: We consider the new divisor 129 and the new remainder 86, and apply the division lemma to get
129 = 86 x 1 + 43
We consider the new divisor 86 and the new remainder 43, and apply the division lemma to get
86 = 43 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 774 and 215 is 43
Notice that 43 = HCF(86,43) = HCF(129,86) = HCF(215,129) = HCF(774,215) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 742 > 43, we apply the division lemma to 742 and 43, to get
742 = 43 x 17 + 11
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 11 and 43, to get
43 = 11 x 3 + 10
Step 3: We consider the new divisor 11 and the new remainder 10, and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 742 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(43,11) = HCF(742,43) .
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Frequently Asked Questions on HCF of 774, 215, 742 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 774, 215, 742?
Answer: HCF of 774, 215, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 215, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 215, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.