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 847, 616, 48 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 847, 616, 48 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 847, 616, 48 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 847, 616, 48 is 1.
HCF(847, 616, 48) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 847, 616, 48 is 1.
Step 1: Since 847 > 616, we apply the division lemma to 847 and 616, to get
847 = 616 x 1 + 231
Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 231 and 616, to get
616 = 231 x 2 + 154
Step 3: We consider the new divisor 231 and the new remainder 154, and apply the division lemma to get
231 = 154 x 1 + 77
We consider the new divisor 154 and the new remainder 77, and apply the division lemma to get
154 = 77 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 77, the HCF of 847 and 616 is 77
Notice that 77 = HCF(154,77) = HCF(231,154) = HCF(616,231) = HCF(847,616) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 48, we apply the division lemma to 77 and 48, to get
77 = 48 x 1 + 29
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 29 and 48, to get
48 = 29 x 1 + 19
Step 3: We consider the new divisor 29 and the new remainder 19, and apply the division lemma to get
29 = 19 x 1 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 77 and 48 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(48,29) = HCF(77,48) .
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 847, 616, 48?
Answer: HCF of 847, 616, 48 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 847, 616, 48 using Euclid's Algorithm?
Answer: For arbitrary numbers 847, 616, 48 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.