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 969, 289, 870 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 969, 289, 870 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 969, 289, 870 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 969, 289, 870 is 1.
HCF(969, 289, 870) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 969, 289, 870 is 1.
Step 1: Since 969 > 289, we apply the division lemma to 969 and 289, to get
969 = 289 x 3 + 102
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 102 and 289, to get
289 = 102 x 2 + 85
Step 3: We consider the new divisor 102 and the new remainder 85, and apply the division lemma to get
102 = 85 x 1 + 17
We consider the new divisor 85 and the new remainder 17, and apply the division lemma to get
85 = 17 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 969 and 289 is 17
Notice that 17 = HCF(85,17) = HCF(102,85) = HCF(289,102) = HCF(969,289) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 17, we apply the division lemma to 870 and 17, to get
870 = 17 x 51 + 3
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 3 and 17, to get
17 = 3 x 5 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
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 17 and 870 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(870,17) .
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 969, 289, 870?
Answer: HCF of 969, 289, 870 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 969, 289, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 969, 289, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.