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 3407, 7164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3407, 7164 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 3407, 7164 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 3407, 7164 is 1.
HCF(3407, 7164) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3407, 7164 is 1.
Step 1: Since 7164 > 3407, we apply the division lemma to 7164 and 3407, to get
7164 = 3407 x 2 + 350
Step 2: Since the reminder 3407 ≠ 0, we apply division lemma to 350 and 3407, to get
3407 = 350 x 9 + 257
Step 3: We consider the new divisor 350 and the new remainder 257, and apply the division lemma to get
350 = 257 x 1 + 93
We consider the new divisor 257 and the new remainder 93,and apply the division lemma to get
257 = 93 x 2 + 71
We consider the new divisor 93 and the new remainder 71,and apply the division lemma to get
93 = 71 x 1 + 22
We consider the new divisor 71 and the new remainder 22,and apply the division lemma to get
71 = 22 x 3 + 5
We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get
22 = 5 x 4 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3407 and 7164 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(71,22) = HCF(93,71) = HCF(257,93) = HCF(350,257) = HCF(3407,350) = HCF(7164,3407) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 3407, 7164?
Answer: HCF of 3407, 7164 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3407, 7164 using Euclid's Algorithm?
Answer: For arbitrary numbers 3407, 7164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.