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 349, 578, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 349, 578, 735 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 349, 578, 735 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 349, 578, 735 is 1.
HCF(349, 578, 735) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 349, 578, 735 is 1.
Step 1: Since 578 > 349, we apply the division lemma to 578 and 349, to get
578 = 349 x 1 + 229
Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 229 and 349, to get
349 = 229 x 1 + 120
Step 3: We consider the new divisor 229 and the new remainder 120, and apply the division lemma to get
229 = 120 x 1 + 109
We consider the new divisor 120 and the new remainder 109,and apply the division lemma to get
120 = 109 x 1 + 11
We consider the new divisor 109 and the new remainder 11,and apply the division lemma to get
109 = 11 x 9 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 349 and 578 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(109,11) = HCF(120,109) = HCF(229,120) = HCF(349,229) = HCF(578,349) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get
735 = 1 x 735 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1
Notice that 1 = HCF(735,1) .
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 349, 578, 735?
Answer: HCF of 349, 578, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 349, 578, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 349, 578, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.