Highest Common Factor of 546, 678, 785 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 546, 678, 785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 678, 785 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 546, 678, 785 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 546, 678, 785 is 1.
HCF(546, 678, 785) = 1
HCF of 546, 678, 785 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 678, 785 is 1.
Highest Common Factor of 546,678,785 is 1
Step 1: Since 678 > 546, we apply the division lemma to 678 and 546, to get
678 = 546 x 1 + 132
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 132 and 546, to get
546 = 132 x 4 + 18
Step 3: We consider the new divisor 132 and the new remainder 18, and apply the division lemma to get
132 = 18 x 7 + 6
We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 546 and 678 is 6
Notice that 6 = HCF(18,6) = HCF(132,18) = HCF(546,132) = HCF(678,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 785 > 6, we apply the division lemma to 785 and 6, to get
785 = 6 x 130 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 785 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(785,6) .
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Frequently Asked Questions on HCF of 546, 678, 785 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 546, 678, 785?
Answer: HCF of 546, 678, 785 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 678, 785 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 678, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
