Highest Common Factor of 970, 371, 688 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 970, 371, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 970, 371, 688 is 1 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 970, 371, 688 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 970, 371, 688 is 1.
HCF(970, 371, 688) = 1
HCF of 970, 371, 688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 970, 371, 688 is 1.
Highest Common Factor of 970,371,688 is 1
Step 1: Since 970 > 371, we apply the division lemma to 970 and 371, to get
970 = 371 x 2 + 228
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 228 and 371, to get
371 = 228 x 1 + 143
Step 3: We consider the new divisor 228 and the new remainder 143, and apply the division lemma to get
228 = 143 x 1 + 85
We consider the new divisor 143 and the new remainder 85,and apply the division lemma to get
143 = 85 x 1 + 58
We consider the new divisor 85 and the new remainder 58,and apply the division lemma to get
85 = 58 x 1 + 27
We consider the new divisor 58 and the new remainder 27,and apply the division lemma to get
58 = 27 x 2 + 4
We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get
27 = 4 x 6 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 970 and 371 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(58,27) = HCF(85,58) = HCF(143,85) = HCF(228,143) = HCF(371,228) = HCF(970,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 1, we apply the division lemma to 688 and 1, to get
688 = 1 x 688 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1
Notice that 1 = HCF(688,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 970, 371, 688 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 970, 371, 688?
Answer: HCF of 970, 371, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 970, 371, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 970, 371, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.