Highest Common Factor of 638, 770, 735 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 638, 770, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 770, 735 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 638, 770, 735 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 638, 770, 735 is 1.
HCF(638, 770, 735) = 1
HCF of 638, 770, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 770, 735 is 1.
Highest Common Factor of 638,770,735 is 1
Step 1: Since 770 > 638, we apply the division lemma to 770 and 638, to get
770 = 638 x 1 + 132
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 132 and 638, to get
638 = 132 x 4 + 110
Step 3: We consider the new divisor 132 and the new remainder 110, and apply the division lemma to get
132 = 110 x 1 + 22
We consider the new divisor 110 and the new remainder 22, and apply the division lemma to get
110 = 22 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 638 and 770 is 22
Notice that 22 = HCF(110,22) = HCF(132,110) = HCF(638,132) = HCF(770,638) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 22, we apply the division lemma to 735 and 22, to get
735 = 22 x 33 + 9
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 9 and 22, to get
22 = 9 x 2 + 4
Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 735 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(735,22) .
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Frequently Asked Questions on HCF of 638, 770, 735 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 638, 770, 735?
Answer: HCF of 638, 770, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 770, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 770, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
