Highest Common Factor of 747, 4164 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 747, 4164 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 747, 4164 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 747, 4164 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 747, 4164 is 3.
HCF(747, 4164) = 3
HCF of 747, 4164 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 747, 4164 is 3.
Highest Common Factor of 747,4164 is 3
Step 1: Since 4164 > 747, we apply the division lemma to 4164 and 747, to get
4164 = 747 x 5 + 429
Step 2: Since the reminder 747 ≠ 0, we apply division lemma to 429 and 747, to get
747 = 429 x 1 + 318
Step 3: We consider the new divisor 429 and the new remainder 318, and apply the division lemma to get
429 = 318 x 1 + 111
We consider the new divisor 318 and the new remainder 111,and apply the division lemma to get
318 = 111 x 2 + 96
We consider the new divisor 111 and the new remainder 96,and apply the division lemma to get
111 = 96 x 1 + 15
We consider the new divisor 96 and the new remainder 15,and apply the division lemma to get
96 = 15 x 6 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 747 and 4164 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(96,15) = HCF(111,96) = HCF(318,111) = HCF(429,318) = HCF(747,429) = HCF(4164,747) .
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Frequently Asked Questions on HCF of 747, 4164 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 747, 4164?
Answer: HCF of 747, 4164 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 747, 4164 using Euclid's Algorithm?
Answer: For arbitrary numbers 747, 4164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.