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 308, 414, 597, 952 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 308, 414, 597, 952 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 308, 414, 597, 952 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 308, 414, 597, 952 is 1.
HCF(308, 414, 597, 952) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 308, 414, 597, 952 is 1.
Step 1: Since 414 > 308, we apply the division lemma to 414 and 308, to get
414 = 308 x 1 + 106
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 106 and 308, to get
308 = 106 x 2 + 96
Step 3: We consider the new divisor 106 and the new remainder 96, and apply the division lemma to get
106 = 96 x 1 + 10
We consider the new divisor 96 and the new remainder 10,and apply the division lemma to get
96 = 10 x 9 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 308 and 414 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(96,10) = HCF(106,96) = HCF(308,106) = HCF(414,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 597 > 2, we apply the division lemma to 597 and 2, to get
597 = 2 x 298 + 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 597 is 1
Notice that 1 = HCF(2,1) = HCF(597,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 952 > 1, we apply the division lemma to 952 and 1, to get
952 = 1 x 952 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 952 is 1
Notice that 1 = HCF(952,1) .
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 308, 414, 597, 952?
Answer: HCF of 308, 414, 597, 952 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 308, 414, 597, 952 using Euclid's Algorithm?
Answer: For arbitrary numbers 308, 414, 597, 952 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.