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 584, 958, 42 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 958, 42 is 2 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 584, 958, 42 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 584, 958, 42 is 2.
HCF(584, 958, 42) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 584, 958, 42 is 2.
Step 1: Since 958 > 584, we apply the division lemma to 958 and 584, to get
958 = 584 x 1 + 374
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 374 and 584, to get
584 = 374 x 1 + 210
Step 3: We consider the new divisor 374 and the new remainder 210, and apply the division lemma to get
374 = 210 x 1 + 164
We consider the new divisor 210 and the new remainder 164,and apply the division lemma to get
210 = 164 x 1 + 46
We consider the new divisor 164 and the new remainder 46,and apply the division lemma to get
164 = 46 x 3 + 26
We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get
46 = 26 x 1 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 584 and 958 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(164,46) = HCF(210,164) = HCF(374,210) = HCF(584,374) = HCF(958,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 2, we apply the division lemma to 42 and 2, to get
42 = 2 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 42 is 2
Notice that 2 = HCF(42,2) .
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 584, 958, 42?
Answer: HCF of 584, 958, 42 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 958, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 958, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.