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 600, 349, 349, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 349, 349, 72 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 600, 349, 349, 72 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 600, 349, 349, 72 is 1.
HCF(600, 349, 349, 72) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 600, 349, 349, 72 is 1.
Step 1: Since 600 > 349, we apply the division lemma to 600 and 349, to get
600 = 349 x 1 + 251
Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 251 and 349, to get
349 = 251 x 1 + 98
Step 3: We consider the new divisor 251 and the new remainder 98, and apply the division lemma to get
251 = 98 x 2 + 55
We consider the new divisor 98 and the new remainder 55,and apply the division lemma to get
98 = 55 x 1 + 43
We consider the new divisor 55 and the new remainder 43,and apply the division lemma to get
55 = 43 x 1 + 12
We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get
43 = 12 x 3 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 600 and 349 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(55,43) = HCF(98,55) = HCF(251,98) = HCF(349,251) = HCF(600,349) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 349 > 1, we apply the division lemma to 349 and 1, to get
349 = 1 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 349 is 1
Notice that 1 = HCF(349,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1
Notice that 1 = HCF(72,1) .
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 600, 349, 349, 72?
Answer: HCF of 600, 349, 349, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 349, 349, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 349, 349, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.