Highest Common Factor of 670, 77 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 670, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 77 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 670, 77 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 670, 77 is 1.
HCF(670, 77) = 1
HCF of 670, 77 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 77 is 1.
Highest Common Factor of 670,77 is 1
Step 1: Since 670 > 77, we apply the division lemma to 670 and 77, to get
670 = 77 x 8 + 54
Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 54 and 77, to get
77 = 54 x 1 + 23
Step 3: We consider the new divisor 54 and the new remainder 23, and apply the division lemma to get
54 = 23 x 2 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 670 and 77 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(54,23) = HCF(77,54) = HCF(670,77) .
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Frequently Asked Questions on HCF of 670, 77 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 670, 77?
Answer: HCF of 670, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.