Highest Common Factor of 5670, 1664 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 5670, 1664 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5670, 1664 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 5670, 1664 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 5670, 1664 is 2.
HCF(5670, 1664) = 2
HCF of 5670, 1664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5670, 1664 is 2.
Highest Common Factor of 5670,1664 is 2
Step 1: Since 5670 > 1664, we apply the division lemma to 5670 and 1664, to get
5670 = 1664 x 3 + 678
Step 2: Since the reminder 1664 ≠ 0, we apply division lemma to 678 and 1664, to get
1664 = 678 x 2 + 308
Step 3: We consider the new divisor 678 and the new remainder 308, and apply the division lemma to get
678 = 308 x 2 + 62
We consider the new divisor 308 and the new remainder 62,and apply the division lemma to get
308 = 62 x 4 + 60
We consider the new divisor 62 and the new remainder 60,and apply the division lemma to get
62 = 60 x 1 + 2
We consider the new divisor 60 and the new remainder 2,and apply the division lemma to get
60 = 2 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5670 and 1664 is 2
Notice that 2 = HCF(60,2) = HCF(62,60) = HCF(308,62) = HCF(678,308) = HCF(1664,678) = HCF(5670,1664) .
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Frequently Asked Questions on HCF of 5670, 1664 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 5670, 1664?
Answer: HCF of 5670, 1664 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5670, 1664 using Euclid's Algorithm?
Answer: For arbitrary numbers 5670, 1664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.