Highest Common Factor of 423, 1107, 1792 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 423, 1107, 1792 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 1107, 1792 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 423, 1107, 1792 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 423, 1107, 1792 is 1.
HCF(423, 1107, 1792) = 1
HCF of 423, 1107, 1792 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 423, 1107, 1792 is 1.
Highest Common Factor of 423,1107,1792 is 1
Step 1: Since 1107 > 423, we apply the division lemma to 1107 and 423, to get
1107 = 423 x 2 + 261
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 261 and 423, to get
423 = 261 x 1 + 162
Step 3: We consider the new divisor 261 and the new remainder 162, and apply the division lemma to get
261 = 162 x 1 + 99
We consider the new divisor 162 and the new remainder 99,and apply the division lemma to get
162 = 99 x 1 + 63
We consider the new divisor 99 and the new remainder 63,and apply the division lemma to get
99 = 63 x 1 + 36
We consider the new divisor 63 and the new remainder 36,and apply the division lemma to get
63 = 36 x 1 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 423 and 1107 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(63,36) = HCF(99,63) = HCF(162,99) = HCF(261,162) = HCF(423,261) = HCF(1107,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1792 > 9, we apply the division lemma to 1792 and 9, to get
1792 = 9 x 199 + 1
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 1 and 9, to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 1792 is 1
Notice that 1 = HCF(9,1) = HCF(1792,9) .
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Frequently Asked Questions on HCF of 423, 1107, 1792 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 423, 1107, 1792?
Answer: HCF of 423, 1107, 1792 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 1107, 1792 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 1107, 1792 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.