Highest Common Factor of 680, 450, 508 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 680, 450, 508 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 450, 508 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 680, 450, 508 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 680, 450, 508 is 2.
HCF(680, 450, 508) = 2
HCF of 680, 450, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 450, 508 is 2.
Highest Common Factor of 680,450,508 is 2
Step 1: Since 680 > 450, we apply the division lemma to 680 and 450, to get
680 = 450 x 1 + 230
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 230 and 450, to get
450 = 230 x 1 + 220
Step 3: We consider the new divisor 230 and the new remainder 220, and apply the division lemma to get
230 = 220 x 1 + 10
We consider the new divisor 220 and the new remainder 10, and apply the division lemma to get
220 = 10 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 680 and 450 is 10
Notice that 10 = HCF(220,10) = HCF(230,220) = HCF(450,230) = HCF(680,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 10, we apply the division lemma to 508 and 10, to get
508 = 10 x 50 + 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 508 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(508,10) .
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Frequently Asked Questions on HCF of 680, 450, 508 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 680, 450, 508?
Answer: HCF of 680, 450, 508 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 450, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 450, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.