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 321, 542, 947 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 321, 542, 947 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 321, 542, 947 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 321, 542, 947 is 1.
HCF(321, 542, 947) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 321, 542, 947 is 1.
Step 1: Since 542 > 321, we apply the division lemma to 542 and 321, to get
542 = 321 x 1 + 221
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 221 and 321, to get
321 = 221 x 1 + 100
Step 3: We consider the new divisor 221 and the new remainder 100, and apply the division lemma to get
221 = 100 x 2 + 21
We consider the new divisor 100 and the new remainder 21,and apply the division lemma to get
100 = 21 x 4 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 321 and 542 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(100,21) = HCF(221,100) = HCF(321,221) = HCF(542,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 947 > 1, we apply the division lemma to 947 and 1, to get
947 = 1 x 947 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 947 is 1
Notice that 1 = HCF(947,1) .
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 321, 542, 947?
Answer: HCF of 321, 542, 947 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 321, 542, 947 using Euclid's Algorithm?
Answer: For arbitrary numbers 321, 542, 947 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.