Highest Common Factor of 148, 684, 513 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 148, 684, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 148, 684, 513 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 148, 684, 513 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 148, 684, 513 is 1.
HCF(148, 684, 513) = 1
HCF of 148, 684, 513 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 148, 684, 513 is 1.
Highest Common Factor of 148,684,513 is 1
Step 1: Since 684 > 148, we apply the division lemma to 684 and 148, to get
684 = 148 x 4 + 92
Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 92 and 148, to get
148 = 92 x 1 + 56
Step 3: We consider the new divisor 92 and the new remainder 56, and apply the division lemma to get
92 = 56 x 1 + 36
We consider the new divisor 56 and the new remainder 36,and apply the division lemma to get
56 = 36 x 1 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 148 and 684 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(92,56) = HCF(148,92) = HCF(684,148) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 4, we apply the division lemma to 513 and 4, to get
513 = 4 x 128 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 513 is 1
Notice that 1 = HCF(4,1) = HCF(513,4) .
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Frequently Asked Questions on HCF of 148, 684, 513 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 148, 684, 513?
Answer: HCF of 148, 684, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 148, 684, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 148, 684, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.