Highest Common Factor of 126, 693, 933 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 126, 693, 933 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 693, 933 is 3 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 126, 693, 933 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 126, 693, 933 is 3.
HCF(126, 693, 933) = 3
HCF of 126, 693, 933 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 693, 933 is 3.
Highest Common Factor of 126,693,933 is 3
Step 1: Since 693 > 126, we apply the division lemma to 693 and 126, to get
693 = 126 x 5 + 63
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 63 and 126, to get
126 = 63 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 63, the HCF of 126 and 693 is 63
Notice that 63 = HCF(126,63) = HCF(693,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 933 > 63, we apply the division lemma to 933 and 63, to get
933 = 63 x 14 + 51
Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 51 and 63, to get
63 = 51 x 1 + 12
Step 3: We consider the new divisor 51 and the new remainder 12, and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 63 and 933 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(933,63) .
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Frequently Asked Questions on HCF of 126, 693, 933 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 126, 693, 933?
Answer: HCF of 126, 693, 933 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 693, 933 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 693, 933 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.