Highest Common Factor of 920, 520, 670 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 920, 520, 670 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 920, 520, 670 is 10 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 920, 520, 670 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 920, 520, 670 is 10.
HCF(920, 520, 670) = 10
HCF of 920, 520, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 920, 520, 670 is 10.
Highest Common Factor of 920,520,670 is 10
Step 1: Since 920 > 520, we apply the division lemma to 920 and 520, to get
920 = 520 x 1 + 400
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 400 and 520, to get
520 = 400 x 1 + 120
Step 3: We consider the new divisor 400 and the new remainder 120, and apply the division lemma to get
400 = 120 x 3 + 40
We consider the new divisor 120 and the new remainder 40, and apply the division lemma to get
120 = 40 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 920 and 520 is 40
Notice that 40 = HCF(120,40) = HCF(400,120) = HCF(520,400) = HCF(920,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 670 > 40, we apply the division lemma to 670 and 40, to get
670 = 40 x 16 + 30
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 30 and 40, to get
40 = 30 x 1 + 10
Step 3: 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 40 and 670 is 10
Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(670,40) .
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Frequently Asked Questions on HCF of 920, 520, 670 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 920, 520, 670?
Answer: HCF of 920, 520, 670 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 920, 520, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 920, 520, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.