Highest Common Factor of 684, 931 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 684, 931 i.e. 19 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 931 is 19 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 684, 931 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 684, 931 is 19.
HCF(684, 931) = 19
HCF of 684, 931 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 931 is 19.
Highest Common Factor of 684,931 is 19
Step 1: Since 931 > 684, we apply the division lemma to 931 and 684, to get
931 = 684 x 1 + 247
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 247 and 684, to get
684 = 247 x 2 + 190
Step 3: We consider the new divisor 247 and the new remainder 190, and apply the division lemma to get
247 = 190 x 1 + 57
We consider the new divisor 190 and the new remainder 57,and apply the division lemma to get
190 = 57 x 3 + 19
We consider the new divisor 57 and the new remainder 19,and apply the division lemma to get
57 = 19 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 684 and 931 is 19
Notice that 19 = HCF(57,19) = HCF(190,57) = HCF(247,190) = HCF(684,247) = HCF(931,684) .
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Frequently Asked Questions on HCF of 684, 931 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 684, 931?
Answer: HCF of 684, 931 is 19 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 931 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 931 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.