Highest Common Factor of 684, 49368 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, 49368 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 49368 is 12 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, 49368 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, 49368 is 12.
HCF(684, 49368) = 12
HCF of 684, 49368 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, 49368 is 12.
Highest Common Factor of 684,49368 is 12
Step 1: Since 49368 > 684, we apply the division lemma to 49368 and 684, to get
49368 = 684 x 72 + 120
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 120 and 684, to get
684 = 120 x 5 + 84
Step 3: We consider the new divisor 120 and the new remainder 84, and apply the division lemma to get
120 = 84 x 1 + 36
We consider the new divisor 84 and the new remainder 36,and apply the division lemma to get
84 = 36 x 2 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 684 and 49368 is 12
Notice that 12 = HCF(36,12) = HCF(84,36) = HCF(120,84) = HCF(684,120) = HCF(49368,684) .
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Frequently Asked Questions on HCF of 684, 49368 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, 49368?
Answer: HCF of 684, 49368 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 49368 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 49368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.