Highest Common Factor of 669, 784 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 669, 784 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 784 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 669, 784 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 669, 784 is 1.
HCF(669, 784) = 1
HCF of 669, 784 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 784 is 1.
Highest Common Factor of 669,784 is 1
Step 1: Since 784 > 669, we apply the division lemma to 784 and 669, to get
784 = 669 x 1 + 115
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 115 and 669, to get
669 = 115 x 5 + 94
Step 3: We consider the new divisor 115 and the new remainder 94, and apply the division lemma to get
115 = 94 x 1 + 21
We consider the new divisor 94 and the new remainder 21,and apply the division lemma to get
94 = 21 x 4 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 669 and 784 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(94,21) = HCF(115,94) = HCF(669,115) = HCF(784,669) .
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Frequently Asked Questions on HCF of 669, 784 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 669, 784?
Answer: HCF of 669, 784 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 784 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.