Highest Common Factor of 746, 584 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 746, 584 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 584 is 2 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 746, 584 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 746, 584 is 2.
HCF(746, 584) = 2
HCF of 746, 584 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 584 is 2.
Highest Common Factor of 746,584 is 2
Step 1: Since 746 > 584, we apply the division lemma to 746 and 584, to get
746 = 584 x 1 + 162
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 162 and 584, to get
584 = 162 x 3 + 98
Step 3: We consider the new divisor 162 and the new remainder 98, and apply the division lemma to get
162 = 98 x 1 + 64
We consider the new divisor 98 and the new remainder 64,and apply the division lemma to get
98 = 64 x 1 + 34
We consider the new divisor 64 and the new remainder 34,and apply the division lemma to get
64 = 34 x 1 + 30
We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 584 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(64,34) = HCF(98,64) = HCF(162,98) = HCF(584,162) = HCF(746,584) .
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Frequently Asked Questions on HCF of 746, 584 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 746, 584?
Answer: HCF of 746, 584 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 584 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.