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 965, 349, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 965, 349, 374 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 965, 349, 374 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 965, 349, 374 is 1.
HCF(965, 349, 374) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 965, 349, 374 is 1.
Step 1: Since 965 > 349, we apply the division lemma to 965 and 349, to get
965 = 349 x 2 + 267
Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 267 and 349, to get
349 = 267 x 1 + 82
Step 3: We consider the new divisor 267 and the new remainder 82, and apply the division lemma to get
267 = 82 x 3 + 21
We consider the new divisor 82 and the new remainder 21,and apply the division lemma to get
82 = 21 x 3 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 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 965 and 349 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(82,21) = HCF(267,82) = HCF(349,267) = HCF(965,349) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 374 > 1, we apply the division lemma to 374 and 1, to get
374 = 1 x 374 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 374 is 1
Notice that 1 = HCF(374,1) .
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 965, 349, 374?
Answer: HCF of 965, 349, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 965, 349, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 965, 349, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.