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 734, 534, 424, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 734, 534, 424, 85 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 734, 534, 424, 85 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 734, 534, 424, 85 is 1.
HCF(734, 534, 424, 85) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 734, 534, 424, 85 is 1.
Step 1: Since 734 > 534, we apply the division lemma to 734 and 534, to get
734 = 534 x 1 + 200
Step 2: Since the reminder 534 ≠ 0, we apply division lemma to 200 and 534, to get
534 = 200 x 2 + 134
Step 3: We consider the new divisor 200 and the new remainder 134, and apply the division lemma to get
200 = 134 x 1 + 66
We consider the new divisor 134 and the new remainder 66,and apply the division lemma to get
134 = 66 x 2 + 2
We consider the new divisor 66 and the new remainder 2,and apply the division lemma to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 734 and 534 is 2
Notice that 2 = HCF(66,2) = HCF(134,66) = HCF(200,134) = HCF(534,200) = HCF(734,534) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 424 > 2, we apply the division lemma to 424 and 2, to get
424 = 2 x 212 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 424 is 2
Notice that 2 = HCF(424,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 2, we apply the division lemma to 85 and 2, to get
85 = 2 x 42 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 85 is 1
Notice that 1 = HCF(2,1) = HCF(85,2) .
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 734, 534, 424, 85?
Answer: HCF of 734, 534, 424, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 734, 534, 424, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 734, 534, 424, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.