Highest Common Factor of 734, 194 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 734, 194 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 734, 194 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 734, 194 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 734, 194 is 2.
HCF(734, 194) = 2
HCF of 734, 194 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 734, 194 is 2.
Highest Common Factor of 734,194 is 2
Step 1: Since 734 > 194, we apply the division lemma to 734 and 194, to get
734 = 194 x 3 + 152
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 152 and 194, to get
194 = 152 x 1 + 42
Step 3: We consider the new divisor 152 and the new remainder 42, and apply the division lemma to get
152 = 42 x 3 + 26
We consider the new divisor 42 and the new remainder 26,and apply the division lemma to get
42 = 26 x 1 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 734 and 194 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(152,42) = HCF(194,152) = HCF(734,194) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 734, 194 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 734, 194?
Answer: HCF of 734, 194 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 734, 194 using Euclid's Algorithm?
Answer: For arbitrary numbers 734, 194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.