Highest Common Factor of 644, 912, 351, 23 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, 912, 351, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 644, 912, 351, 23 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 644, 912, 351, 23 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, 912, 351, 23 is 1.
HCF(644, 912, 351, 23) = 1
HCF of 644, 912, 351, 23 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, 912, 351, 23 is 1.
Highest Common Factor of 644,912,351,23 is 1
Step 1: Since 912 > 644, we apply the division lemma to 912 and 644, to get
912 = 644 x 1 + 268
Step 2: Since the reminder 644 ≠ 0, we apply division lemma to 268 and 644, to get
644 = 268 x 2 + 108
Step 3: We consider the new divisor 268 and the new remainder 108, and apply the division lemma to get
268 = 108 x 2 + 52
We consider the new divisor 108 and the new remainder 52,and apply the division lemma to get
108 = 52 x 2 + 4
We consider the new divisor 52 and the new remainder 4,and apply the division lemma to get
52 = 4 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 644 and 912 is 4
Notice that 4 = HCF(52,4) = HCF(108,52) = HCF(268,108) = HCF(644,268) = HCF(912,644) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 351 > 4, we apply the division lemma to 351 and 4, to get
351 = 4 x 87 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 351 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(351,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 1, we apply the division lemma to 23 and 1, to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 23 is 1
Notice that 1 = HCF(23,1) .
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Frequently Asked Questions on HCF of 644, 912, 351, 23 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, 912, 351, 23?
Answer: HCF of 644, 912, 351, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 644, 912, 351, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 644, 912, 351, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.