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, 973, 634 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 973, 634 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, 973, 634 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, 973, 634 is 1.
HCF(546, 973, 634) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 973, 634 is 1.
Step 1: Since 973 > 546, we apply the division lemma to 973 and 546, to get
973 = 546 x 1 + 427
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 427 and 546, to get
546 = 427 x 1 + 119
Step 3: We consider the new divisor 427 and the new remainder 119, and apply the division lemma to get
427 = 119 x 3 + 70
We consider the new divisor 119 and the new remainder 70,and apply the division lemma to get
119 = 70 x 1 + 49
We consider the new divisor 70 and the new remainder 49,and apply the division lemma to get
70 = 49 x 1 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 546 and 973 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(70,49) = HCF(119,70) = HCF(427,119) = HCF(546,427) = HCF(973,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 634 > 7, we apply the division lemma to 634 and 7, to get
634 = 7 x 90 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 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 7 and 634 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(634,7) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 973, 634?
Answer: HCF of 546, 973, 634 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 973, 634 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 973, 634 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.