Highest Common Factor of 684, 504, 342 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, 504, 342 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 504, 342 is 18 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, 504, 342 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, 504, 342 is 18.
HCF(684, 504, 342) = 18
HCF of 684, 504, 342 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, 504, 342 is 18.
Highest Common Factor of 684,504,342 is 18
Step 1: Since 684 > 504, we apply the division lemma to 684 and 504, to get
684 = 504 x 1 + 180
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 180 and 504, to get
504 = 180 x 2 + 144
Step 3: We consider the new divisor 180 and the new remainder 144, and apply the division lemma to get
180 = 144 x 1 + 36
We consider the new divisor 144 and the new remainder 36, and apply the division lemma to get
144 = 36 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 684 and 504 is 36
Notice that 36 = HCF(144,36) = HCF(180,144) = HCF(504,180) = HCF(684,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 36, we apply the division lemma to 342 and 36, to get
342 = 36 x 9 + 18
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 18 and 36, to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 36 and 342 is 18
Notice that 18 = HCF(36,18) = HCF(342,36) .
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Frequently Asked Questions on HCF of 684, 504, 342 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, 504, 342?
Answer: HCF of 684, 504, 342 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 504, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 504, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
