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 338, 953, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 953, 677 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 338, 953, 677 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 338, 953, 677 is 1.
HCF(338, 953, 677) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 953, 677 is 1.
Step 1: Since 953 > 338, we apply the division lemma to 953 and 338, to get
953 = 338 x 2 + 277
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 277 and 338, to get
338 = 277 x 1 + 61
Step 3: We consider the new divisor 277 and the new remainder 61, and apply the division lemma to get
277 = 61 x 4 + 33
We consider the new divisor 61 and the new remainder 33,and apply the division lemma to get
61 = 33 x 1 + 28
We consider the new divisor 33 and the new remainder 28,and apply the division lemma to get
33 = 28 x 1 + 5
We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get
28 = 5 x 5 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 338 and 953 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(33,28) = HCF(61,33) = HCF(277,61) = HCF(338,277) = HCF(953,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 1, we apply the division lemma to 677 and 1, to get
677 = 1 x 677 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 677 is 1
Notice that 1 = HCF(677,1) .
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 338, 953, 677?
Answer: HCF of 338, 953, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 953, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 953, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.