Highest Common Factor of 730, 840, 638, 996 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 730, 840, 638, 996 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 730, 840, 638, 996 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 730, 840, 638, 996 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 730, 840, 638, 996 is 2.
HCF(730, 840, 638, 996) = 2
HCF of 730, 840, 638, 996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 730, 840, 638, 996 is 2.
Highest Common Factor of 730,840,638,996 is 2
Step 1: Since 840 > 730, we apply the division lemma to 840 and 730, to get
840 = 730 x 1 + 110
Step 2: Since the reminder 730 ≠ 0, we apply division lemma to 110 and 730, to get
730 = 110 x 6 + 70
Step 3: We consider the new divisor 110 and the new remainder 70, and apply the division lemma to get
110 = 70 x 1 + 40
We consider the new divisor 70 and the new remainder 40,and apply the division lemma to get
70 = 40 x 1 + 30
We consider the new divisor 40 and the new remainder 30,and apply the division lemma to get
40 = 30 x 1 + 10
We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 730 and 840 is 10
Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(70,40) = HCF(110,70) = HCF(730,110) = HCF(840,730) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 638 > 10, we apply the division lemma to 638 and 10, to get
638 = 10 x 63 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 638 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(638,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 996 > 2, we apply the division lemma to 996 and 2, to get
996 = 2 x 498 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 996 is 2
Notice that 2 = HCF(996,2) .
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Frequently Asked Questions on HCF of 730, 840, 638, 996 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 730, 840, 638, 996?
Answer: HCF of 730, 840, 638, 996 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 730, 840, 638, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 730, 840, 638, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.