Highest Common Factor of 60, 90, 680, 322 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 60, 90, 680, 322 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 90, 680, 322 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 60, 90, 680, 322 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 60, 90, 680, 322 is 2.
HCF(60, 90, 680, 322) = 2
HCF of 60, 90, 680, 322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 60, 90, 680, 322 is 2.
Highest Common Factor of 60,90,680,322 is 2
Step 1: Since 90 > 60, we apply the division lemma to 90 and 60, to get
90 = 60 x 1 + 30
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 30 and 60, to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 60 and 90 is 30
Notice that 30 = HCF(60,30) = HCF(90,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 30, we apply the division lemma to 680 and 30, to get
680 = 30 x 22 + 20
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 20 and 30, to get
30 = 20 x 1 + 10
Step 3: We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 30 and 680 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(680,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 322 > 10, we apply the division lemma to 322 and 10, to get
322 = 10 x 32 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 322 is 2
Notice that 2 = HCF(10,2) = HCF(322,10) .
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Frequently Asked Questions on HCF of 60, 90, 680, 322 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 60, 90, 680, 322?
Answer: HCF of 60, 90, 680, 322 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 90, 680, 322 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 90, 680, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.