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 769, 3394, 4354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 769, 3394, 4354 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 769, 3394, 4354 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 769, 3394, 4354 is 1.
HCF(769, 3394, 4354) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 769, 3394, 4354 is 1.
Step 1: Since 3394 > 769, we apply the division lemma to 3394 and 769, to get
3394 = 769 x 4 + 318
Step 2: Since the reminder 769 ≠ 0, we apply division lemma to 318 and 769, to get
769 = 318 x 2 + 133
Step 3: We consider the new divisor 318 and the new remainder 133, and apply the division lemma to get
318 = 133 x 2 + 52
We consider the new divisor 133 and the new remainder 52,and apply the division lemma to get
133 = 52 x 2 + 29
We consider the new divisor 52 and the new remainder 29,and apply the division lemma to get
52 = 29 x 1 + 23
We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get
29 = 23 x 1 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 769 and 3394 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(52,29) = HCF(133,52) = HCF(318,133) = HCF(769,318) = HCF(3394,769) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4354 > 1, we apply the division lemma to 4354 and 1, to get
4354 = 1 x 4354 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4354 is 1
Notice that 1 = HCF(4354,1) .
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 769, 3394, 4354?
Answer: HCF of 769, 3394, 4354 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 769, 3394, 4354 using Euclid's Algorithm?
Answer: For arbitrary numbers 769, 3394, 4354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.