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 759, 974, 334 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 759, 974, 334 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 759, 974, 334 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 759, 974, 334 is 1.
HCF(759, 974, 334) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 759, 974, 334 is 1.
Step 1: Since 974 > 759, we apply the division lemma to 974 and 759, to get
974 = 759 x 1 + 215
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 215 and 759, to get
759 = 215 x 3 + 114
Step 3: We consider the new divisor 215 and the new remainder 114, and apply the division lemma to get
215 = 114 x 1 + 101
We consider the new divisor 114 and the new remainder 101,and apply the division lemma to get
114 = 101 x 1 + 13
We consider the new divisor 101 and the new remainder 13,and apply the division lemma to get
101 = 13 x 7 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 759 and 974 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(101,13) = HCF(114,101) = HCF(215,114) = HCF(759,215) = HCF(974,759) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 334 > 1, we apply the division lemma to 334 and 1, to get
334 = 1 x 334 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 334 is 1
Notice that 1 = HCF(334,1) .
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 759, 974, 334?
Answer: HCF of 759, 974, 334 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 759, 974, 334 using Euclid's Algorithm?
Answer: For arbitrary numbers 759, 974, 334 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.