Highest Common Factor of 732, 868, 431 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 732, 868, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 732, 868, 431 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 732, 868, 431 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 732, 868, 431 is 1.
HCF(732, 868, 431) = 1
HCF of 732, 868, 431 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 732, 868, 431 is 1.
Highest Common Factor of 732,868,431 is 1
Step 1: Since 868 > 732, we apply the division lemma to 868 and 732, to get
868 = 732 x 1 + 136
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 136 and 732, to get
732 = 136 x 5 + 52
Step 3: We consider the new divisor 136 and the new remainder 52, and apply the division lemma to get
136 = 52 x 2 + 32
We consider the new divisor 52 and the new remainder 32,and apply the division lemma to get
52 = 32 x 1 + 20
We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get
32 = 20 x 1 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 732 and 868 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(52,32) = HCF(136,52) = HCF(732,136) = HCF(868,732) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 431 > 4, we apply the division lemma to 431 and 4, to get
431 = 4 x 107 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: 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 4 and 431 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(431,4) .
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Frequently Asked Questions on HCF of 732, 868, 431 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 732, 868, 431?
Answer: HCF of 732, 868, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 732, 868, 431 using Euclid's Algorithm?
Answer: For arbitrary numbers 732, 868, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.