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 850, 524, 160 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 850, 524, 160 is 2 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 850, 524, 160 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 850, 524, 160 is 2.
HCF(850, 524, 160) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 850, 524, 160 is 2.
Step 1: Since 850 > 524, we apply the division lemma to 850 and 524, to get
850 = 524 x 1 + 326
Step 2: Since the reminder 524 ≠ 0, we apply division lemma to 326 and 524, to get
524 = 326 x 1 + 198
Step 3: We consider the new divisor 326 and the new remainder 198, and apply the division lemma to get
326 = 198 x 1 + 128
We consider the new divisor 198 and the new remainder 128,and apply the division lemma to get
198 = 128 x 1 + 70
We consider the new divisor 128 and the new remainder 70,and apply the division lemma to get
128 = 70 x 1 + 58
We consider the new divisor 70 and the new remainder 58,and apply the division lemma to get
70 = 58 x 1 + 12
We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 850 and 524 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(128,70) = HCF(198,128) = HCF(326,198) = HCF(524,326) = HCF(850,524) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 2, we apply the division lemma to 160 and 2, to get
160 = 2 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 160 is 2
Notice that 2 = HCF(160,2) .
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 850, 524, 160?
Answer: HCF of 850, 524, 160 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 850, 524, 160 using Euclid's Algorithm?
Answer: For arbitrary numbers 850, 524, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.