Highest Common Factor of 520, 840, 738, 910 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 520, 840, 738, 910 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 520, 840, 738, 910 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 520, 840, 738, 910 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 520, 840, 738, 910 is 2.
HCF(520, 840, 738, 910) = 2
HCF of 520, 840, 738, 910 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 520, 840, 738, 910 is 2.
Highest Common Factor of 520,840,738,910 is 2
Step 1: Since 840 > 520, we apply the division lemma to 840 and 520, to get
840 = 520 x 1 + 320
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 320 and 520, to get
520 = 320 x 1 + 200
Step 3: We consider the new divisor 320 and the new remainder 200, and apply the division lemma to get
320 = 200 x 1 + 120
We consider the new divisor 200 and the new remainder 120,and apply the division lemma to get
200 = 120 x 1 + 80
We consider the new divisor 120 and the new remainder 80,and apply the division lemma to get
120 = 80 x 1 + 40
We consider the new divisor 80 and the new remainder 40,and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 520 and 840 is 40
Notice that 40 = HCF(80,40) = HCF(120,80) = HCF(200,120) = HCF(320,200) = HCF(520,320) = HCF(840,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 738 > 40, we apply the division lemma to 738 and 40, to get
738 = 40 x 18 + 18
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 18 and 40, to get
40 = 18 x 2 + 4
Step 3: We consider the new divisor 18 and the new remainder 4, and apply the division lemma to get
18 = 4 x 4 + 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 40 and 738 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(738,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 910 > 2, we apply the division lemma to 910 and 2, to get
910 = 2 x 455 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 910 is 2
Notice that 2 = HCF(910,2) .
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Frequently Asked Questions on HCF of 520, 840, 738, 910 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 520, 840, 738, 910?
Answer: HCF of 520, 840, 738, 910 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 520, 840, 738, 910 using Euclid's Algorithm?
Answer: For arbitrary numbers 520, 840, 738, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.