Highest Common Factor of 644, 774, 156 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 644, 774, 156 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 644, 774, 156 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 644, 774, 156 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 644, 774, 156 is 2.
HCF(644, 774, 156) = 2
HCF of 644, 774, 156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 644, 774, 156 is 2.
Highest Common Factor of 644,774,156 is 2
Step 1: Since 774 > 644, we apply the division lemma to 774 and 644, to get
774 = 644 x 1 + 130
Step 2: Since the reminder 644 ≠ 0, we apply division lemma to 130 and 644, to get
644 = 130 x 4 + 124
Step 3: We consider the new divisor 130 and the new remainder 124, and apply the division lemma to get
130 = 124 x 1 + 6
We consider the new divisor 124 and the new remainder 6,and apply the division lemma to get
124 = 6 x 20 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 644 and 774 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(124,6) = HCF(130,124) = HCF(644,130) = HCF(774,644) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 156 > 2, we apply the division lemma to 156 and 2, to get
156 = 2 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 156 is 2
Notice that 2 = HCF(156,2) .
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Frequently Asked Questions on HCF of 644, 774, 156 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 644, 774, 156?
Answer: HCF of 644, 774, 156 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 644, 774, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 644, 774, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.