Highest Common Factor of 660, 970, 680 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 660, 970, 680 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 970, 680 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 660, 970, 680 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 660, 970, 680 is 10.
HCF(660, 970, 680) = 10
HCF of 660, 970, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 970, 680 is 10.
Highest Common Factor of 660,970,680 is 10
Step 1: Since 970 > 660, we apply the division lemma to 970 and 660, to get
970 = 660 x 1 + 310
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 310 and 660, to get
660 = 310 x 2 + 40
Step 3: We consider the new divisor 310 and the new remainder 40, and apply the division lemma to get
310 = 40 x 7 + 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 660 and 970 is 10
Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(310,40) = HCF(660,310) = HCF(970,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 10, we apply the division lemma to 680 and 10, to get
680 = 10 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 680 is 10
Notice that 10 = HCF(680,10) .
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Frequently Asked Questions on HCF of 660, 970, 680 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 660, 970, 680?
Answer: HCF of 660, 970, 680 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 970, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 970, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
