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 497, 308, 219, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 497, 308, 219, 61 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 497, 308, 219, 61 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 497, 308, 219, 61 is 1.
HCF(497, 308, 219, 61) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 497, 308, 219, 61 is 1.
Step 1: Since 497 > 308, we apply the division lemma to 497 and 308, to get
497 = 308 x 1 + 189
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 189 and 308, to get
308 = 189 x 1 + 119
Step 3: We consider the new divisor 189 and the new remainder 119, and apply the division lemma to get
189 = 119 x 1 + 70
We consider the new divisor 119 and the new remainder 70,and apply the division lemma to get
119 = 70 x 1 + 49
We consider the new divisor 70 and the new remainder 49,and apply the division lemma to get
70 = 49 x 1 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 497 and 308 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(70,49) = HCF(119,70) = HCF(189,119) = HCF(308,189) = HCF(497,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 219 > 7, we apply the division lemma to 219 and 7, to get
219 = 7 x 31 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 7 and 219 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(219,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 1, we apply the division lemma to 61 and 1, to get
61 = 1 x 61 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 61 is 1
Notice that 1 = HCF(61,1) .
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 497, 308, 219, 61?
Answer: HCF of 497, 308, 219, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 497, 308, 219, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 497, 308, 219, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.