Highest Common Factor of 723, 924, 714, 408 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 723, 924, 714, 408 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 924, 714, 408 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 723, 924, 714, 408 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 723, 924, 714, 408 is 3.
HCF(723, 924, 714, 408) = 3
HCF of 723, 924, 714, 408 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 924, 714, 408 is 3.
Highest Common Factor of 723,924,714,408 is 3
Step 1: Since 924 > 723, we apply the division lemma to 924 and 723, to get
924 = 723 x 1 + 201
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 201 and 723, to get
723 = 201 x 3 + 120
Step 3: We consider the new divisor 201 and the new remainder 120, and apply the division lemma to get
201 = 120 x 1 + 81
We consider the new divisor 120 and the new remainder 81,and apply the division lemma to get
120 = 81 x 1 + 39
We consider the new divisor 81 and the new remainder 39,and apply the division lemma to get
81 = 39 x 2 + 3
We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 723 and 924 is 3
Notice that 3 = HCF(39,3) = HCF(81,39) = HCF(120,81) = HCF(201,120) = HCF(723,201) = HCF(924,723) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 714 > 3, we apply the division lemma to 714 and 3, to get
714 = 3 x 238 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 714 is 3
Notice that 3 = HCF(714,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 3, we apply the division lemma to 408 and 3, to get
408 = 3 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 408 is 3
Notice that 3 = HCF(408,3) .
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Frequently Asked Questions on HCF of 723, 924, 714, 408 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 723, 924, 714, 408?
Answer: HCF of 723, 924, 714, 408 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 924, 714, 408 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 924, 714, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.