Highest Common Factor of 670, 778 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, 778 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 778 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 670, 778 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, 778 is 2.
HCF(670, 778) = 2
HCF of 670, 778 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, 778 is 2.
Highest Common Factor of 670,778 is 2
Step 1: Since 778 > 670, we apply the division lemma to 778 and 670, to get
778 = 670 x 1 + 108
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 108 and 670, to get
670 = 108 x 6 + 22
Step 3: We consider the new divisor 108 and the new remainder 22, and apply the division lemma to get
108 = 22 x 4 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 670 and 778 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(108,22) = HCF(670,108) = HCF(778,670) .
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Frequently Asked Questions on HCF of 670, 778 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, 778?
Answer: HCF of 670, 778 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 778 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.