Highest Common Factor of 3408, 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 3408, 778 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3408, 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 3408, 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 3408, 778 is 2.
HCF(3408, 778) = 2
HCF of 3408, 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 3408, 778 is 2.
Highest Common Factor of 3408,778 is 2
Step 1: Since 3408 > 778, we apply the division lemma to 3408 and 778, to get
3408 = 778 x 4 + 296
Step 2: Since the reminder 778 ≠ 0, we apply division lemma to 296 and 778, to get
778 = 296 x 2 + 186
Step 3: We consider the new divisor 296 and the new remainder 186, and apply the division lemma to get
296 = 186 x 1 + 110
We consider the new divisor 186 and the new remainder 110,and apply the division lemma to get
186 = 110 x 1 + 76
We consider the new divisor 110 and the new remainder 76,and apply the division lemma to get
110 = 76 x 1 + 34
We consider the new divisor 76 and the new remainder 34,and apply the division lemma to get
76 = 34 x 2 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3408 and 778 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(76,34) = HCF(110,76) = HCF(186,110) = HCF(296,186) = HCF(778,296) = HCF(3408,778) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3408, 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 3408, 778?
Answer: HCF of 3408, 778 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3408, 778 using Euclid's Algorithm?
Answer: For arbitrary numbers 3408, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.